G9 asset classes,by dev-job mkt depth

Beware many big domains don’t need lots of developers.

  1. Bonds including sovereign
  2. [V] Eq (including ETF) cash and swap
  3. [V] FX cash and fwd
  4. Eq/FX options
  5. [Q] IRS
  6. IR (including bond) futures
  7. [Q] CDS
  8. [Q] MBS
  9. [d=will see higher demand for developers??]
  10. [V=volume and velocity drive the demand for developers]
  11. [Q=low volume but j4 automation is quantitative in terms of automated risk and pricing.] I believe these quantitative asset classes play to my “theoretical” strength and not too niche, but these domains aren’t growing.

fractional shares: quite common]basket trading

https://www.investopedia.com/terms/f/fractionalshare.asp explains that fractional shares can be naturally-occurring, but I want to talk about artificial fractional shares in “normal” stocks.

Custom baskets are traded as equity-swaps. Client specify a weightage profile of the basket like x% IBM + y% AAPL + z% GE where x+y+z ==100. The sell-side dealer (not a broker) would hold the positions on its own book, but on behalf of clients.

Such a basket is not listed on any exchange (unlike ETFs). If client were to go long such a basket directly, due to limited liquidity on some constituent stocks she may not get the desired weightage. In contrast, a sell-side has more liquidity access including smart-order-routers and internal execution.

The weightage means some stocks will have fractional quantities in a given basket. Also such a basket could be too big in dollar amount like $58,476, so the sell-side often use a divisor (like 584) to create a unit price of $100, similar to a share’s price in a mutual fund. Fractional quantities are even more inevitable in one unit or in 391 units.

After a client buys 391 units she could sell partially.

With mutual funds, I often buy fractional units as well, like 391.52 units.

ibank: trade book`against exch and against client

In an ibank equity trading system, every (partial or full) fill seems to be booked twice

  1. as a trade against a client
  2. as a trade against an exchange

I think this is because the ibank, not the client, is a member of the exchange, even though the client is typically a big buy-side like a hedge fund or asset manager.

The booking system must be reconciled with the exchange. The exchange’s booking only shows the ibank as the counterparty (the opposite counterparty is the exchange itself.) Therefore the ibank must record one trade as “ibank vs exchange”

That means the “ibank vs client” trade has to be booked separately.

Q: how about bonds?
A: I believe the ibank is a dealer rather than a broker. Using internal inventory, the ibank can execute a trade against client, without a corresponding trade on ECN.

Q: how about forex?
A: I think there’s less standardization here. No forex ECN “takes the opposite side of every single trade” as exchanges do. Forex is typically a dealer’s market, similar to bonds. However for spot FX, dealers usually maintain low inventory and executes an ECN trade for every client trade. Biggest FX dealers are banks with huge inventory, but still relative small compared to the daily trade volume.

risk-neutral means..illustrated by CIP

Background — all of my valuation procedures are subjective, like valuing a property, an oil field, a commodity …

Risk-Neutral has always been confusing, vague, abstract to me. CIP ^ UIP, based on Mark Hendricks notes has an illustration —

  • RN means .. regardless of individuals’ risk profiles … therefore objective
  • RN means .. partially [1] backed by arbitrage arguments, but often theoretical
    • [1] partially can mean 30% or 80%
    • If it’s well supported by arbitrage argument, then replication becomes theoretical foundation of RN pricing


aggregation unit

I now believe there are at least two purposes, not necessarily reflected in any systems I worked on.

  • Purpose: FINRA regulatory reporting on aggregate short positions on a given stock like AAPL. Probably under Regulation SHO
  • Purpose: Self trades (also wash trades) that create a false impression of activity. I believe trading volume for AAPL would be artificially inflated by these trades. “Bona fide” trade reporting is expected. To deal with self-trades, a firm need to exclude them in trade reporting. But what if a self-trade involves two trading accounts or two algorithms? Are the two systems completely unrelated (therefore not self-trade) or both come under a single umbrella (therefore self-trade)? That’s why we assign an “aggregation unit” to each account. If the two accounts share an AggUnit then yes self-trade.

Are equities simpler than FICC@@

I agree that FICC products are more complex, even if we exclude derivatives

  • FI product valuations are sensitive to multiple factors such as yield curve, credit spread
  • FI products all have an expiry date
  • We often calculate a theoretical price since market price is often unavailable or illiquid.
  • I will omit other reasons, because I want to talk more (but not too much) about …

I see some complexities (mostly) specific to equities. Disclaimer — I have only a short few years of experience in this space. Some of the complexities here may not be complex in many systems but may be artificially, unnecessarily complex in one specific system. Your mileage may vary.

  • Many regulatory requirements, not all straightforward
  • Restrictions – Bloomberg publishes many types of restrictions for each stock
  • Short sale — Many rules and processes around short sale
  • Benchmarks, Execution algorithms and alphas. HFT is mostly on equities (+ some FX pairs)
  • Market impact – is a non-trivial topic for quants
  • Closing auctions and opening auctions
  • Market microstructure
  • Order books – are valuable, not easy to replicate, and change by the second
  • Many orders in a published order book get cancelled quickly. I think some highly liquid government bonds may have similar features
  • Many small rules about commission and exchange fees
  • Aggregate exposure — to a single stock… aggregation across accounts is a challenge mostly in equities since there are so many trades. You often lose track of your aggregate exposure.
  • Exchange connectivity
  • Order routing
  • Order management

custom-basket ^ portflio trading

A client can ask a broker to buy “two IBM, one MSFT” either as a AA) custom basket or a BB) portfolio. The broker handles the two differently.

Only the Basket (not the portfolio) is “listed” on Bloomberg (but not on any exchanges). Client can see the pricing details in Bloomberg terminal, with a unique basket identifier.

Booking — the basket trade is recorded as a single indivisible position; whereas the portfolio trade gets booked as individual positions. Client can only sell the entire basket; whereas the portfolio client can sell individual component stocks.

Fees — There is only one brokerage fee for the basket, but 5 for a portfolio of 5 stocks.

The broker or investment advisor often has a “view” and advice on a given basket.

Corporate actions should be handled in the basket automatically.

I feel portfolio is more flexible, more informal than custom basket which is less formalized, less regulated than an index-tracking ETF.

swap on eq futures/options: client motive

Q1: why would anyone want to enter a swap contract on an option/futures (such a complex structure) rather than trading the option/futures directly?

Q2: why would anyone want to use swap on an offshore stock rather than trading it directly?

More fundamentally,

Q3: why would anyone want to use swap on domestic stock?

A1: I believe one important motivation is restrictions/regulation.  A trading shop needs a lot of approvals, licenses, capital, disclosures … to trade on a given futures/options exchange. I guess there might be disclosure and statuary reporting requirements.  If the shop can’t or doesn’t want to bother with the regulations, they can achieve the same exposure via a swap contract.

This is esp. relevant in cross-border trading. Many regulators restrict access by offshore traders, as a way to protect the local market and local investors.

A3: One possible reason is transparency, disclosure and reporting. I guess many shops don’t want to disclose their positions in, say, AAPL. The swap contract can help them conceal their position.

FRA^ED-fut: actual loan-rate fixed when@@

Suppose I’m IBM, and need to borrow in 3 months’s time. As explained in typical FRA scenario, inspired by CFA Reading 71, I could buy a FRA and agree to pay a pre-agreed rate of 550 bps.  What’s the actual loan rate? As explained in that post,

  • If I borrow on open market, then actual loan rate is the open-market rate on 1 Apr
  • If I borrow from the FRA dealer GS, then loan rate is the pre-agreed 550 bps
  • Either way, I’m indifferent, since in the open-market case, what ever rate I pay is offset by the p/l of the FRA

Instead of FRA, I could go short the eurodollar futures. This contract is always cash-settled, so the actually loan rate is probably the open-market rate, but whatever market rate I pay is offset by the p/l of the futures contract.

swap^cash equity trade: key differences

I now feel an equity swap is an OTC contract; whereas an IBM cash buy/sell is executed on the exchange.

  • When a swap trade settles, the client has established a contract with a Dealer. It’s a binding bilateral contract having an expiry, and possibly collateral. You can’t easily transfer the contract.
  • When a cash trade settles, the client has ownership of 500 IBM shares. No contract. No counterparty. No expiry. No dealer.

I think a cash trade is like buying a house. Your ownership is registered with the government. You an transfer the ownership easily.

In contrast, if you own a share in coop or a REIT or a real-estate private equity, you have a contract with a company as the counterparty.

Before a dealer accepts you as a swap trading partner, you must be a major company to qualify to be counterparty of a binding contract. A retail investor won’t qualify.

ETF mkt maker #RBC

The market maker (a dealer) does mostly prop trading, with very light client flow.

Q1: creation/redemption of units?
A: yes the ETF market maker participates in those. When the dealer has bought lots of underlier stocks, it would create units; when the dealer has bought a large inventory of units, it would redeem them (convert to underliers)

Q1b: what’s the motivation for dealer to do that?
A: there’s profit to be made

Q3: restrictions on short position held by a dealer?
A: there are restrictions on how long you can hold a short position without a borrow (stock loan). For regular investors it could be a few days or within 0 sec. For a market maker, it is definitely longer, like 5 days

Q3b: how about size of the short position?
A: probably not. However, if a dealer has a huge short position and looking for a borrow, the stock loan could be very expensive.

Q: how is the bid or ask price decided in the market maker system? Is it similar to the citi muni system? In a competitive, highly liquid market, demand is sensitive to price.
A: fairly simple because the underliers’ bid/ask are well-known and tight. For a bond ETF, the spread is bigger.
A: inventory level in the dealer’s account is another factor
A: pressure in the market micro-structure is another factor. If you see heavy bidding and few offers, then you may predict price rise

share buy-back #basics

  • shares outstanding — reduced, since the repurchased shares (say 100M out of 500M total outstanding) is no longer available for trading.
  • Who pays cash to who? Company pays existing public shareholders (buying on the open market), so company need to pay out hard cash! Will reduce company’s cash position.
  • EPS — benefits, leading to immediate price appreciation
  • Total assets — reduces, improving ROA/ROE
  • Demonstrates comfortable cash position
  • Initiated by — Management when they think it is undervalued
  • Perhaps requested by — Existing share holder hoping to make a profit
  • company has excess capital and
  • A.k.a “share repurchase”

compute FX swap bid/ask quotes from spotFX+IR quotes #eg calc

Trac Consultancy’s coursebook has an example —

USD/IDR spot = 9150 / 9160
1m USD = 2.375% / 2.5%
1m IDR = 6.125% / 6.25%

Q: USD/IDR forward outright = ? / ?

Rule 1: treat first currency (i.e. USD) as a commodity like silver. Like all currency commodities, this one has a positive carry i.e. interest.

Rule 2: Immediately, notice our silver earns lower interest than IDR, so silver is at fwd Premium, i.e. fwd price must be higher than spot.

Rule 3: in a simple zero-spread context, we know fwd price = spot * (1 + interest differential). This same formula still holds, but now we need to decide which spot bid/ask to use, which 1m-USD bid/ask to use, which 1m-IDR bid/ask to use.

Let’s say we want to compute the fwd _b_i_d_ price (rather than the ask) of the silver. The only fulfillment mechanism is — We the sell-side would borrow IDR, buy silver, lend the silver. At maturity, the total amount of silver divided by the amount of IDR would be same as my fwd bid price. In these 3 trades, we the sell-side would NOT cross the bid/ask spread even once, so we always use the favorable side of bid/ask, meaning

Use the Lower 1m-IDR
Use the Lower spot silver price
Use the Higher 1m-silver

Therefore fwd bid = 9150 [1 + (6.125%-2.5%)/12] = 9178

…… That’s the conclusion. Let’s reflect —

Rule 4: if we arrange the 4 numbers ascending – 2.375 / 2.5 / 6.125 / 6.25 then we always get interest differential between … either the middle pair (6.125-2.5) OR the outside pair (6.25-2.375). This is because the dealer always uses the favorable quote of the lend and borrow.

Rule 5: We are working out the bid side, which is always lower than ask, so the spot quote to use has to be the bid. If the spot ask were used, it could be so much higher than the other side (for an illiquid pair) that the final fwd bid price is higher than the fwd ask! In fact this echos Rule 9 below.

Rule 5b: once we acquire the silver, we always lend it at the ask (i.e. 2.5). From Rule 4, the interest differential is (6.125-2.5)

Rule 9: As a dealer/sell-side, always pick the favorable side when picking the spot, the IR on ccy1 and IR on ccy2.  If at any step you were to pick the unfavorable number, that number could be so extreme (huge bid/ask spread exists) as to make the final fwd bid Exceed the ask.

Let’s apply the rules on the fwd _a_s_k_ = 9160 [ 1+ (6.25% – 2.375%)/12 ] = 9190

Rule 1/2/3/4 same.

Apply Rule 5 – use spot ask (which is the higher quote). Once we sell silver spot, we lend the IDR sales proceeds at the higher side which is 6.25%….

cross-currency equity swap: %%intuition

Trade 1: At Time 1, CK (a hedge fund based in Japan) buys one share of GE priced at USD 10, paying JPY 1000. Eleven months later, GE is still at USD 10 which is now JPY 990. CK faces a paper loss due to FX. I will treat USD as asset currency. CK bought 10 greenbacks at 100 yen each and now each greenback is worth 99 yen only.

Trade 2: a comparable single-currency eq-swap trade

Trade 3: a comparable x-ccy swap. At Time 1, the dealer (say GS) buys and holds GE on client’s behalf.

(It is instructive to compare this to compare this to Trade 2. The only difference is the FX.)

In Trade 3, how did GS pay to acquire the share? GS received JPY 1000 from CK and used it to get [1] 10 greenbacks to pay for the stock.

Q: What (standard) solutions do GS have to eliminate its own FX risk and remain transparent to client? I think GS must pass on the FX risk to client.

I think in any x-ccy deal with a dealer bank, this FX risk is unavoidable for CK. Bank always avoids the FX risk and transfer the risk to client.

[1] GS probably bought USDJPY on the street. Who GS bought from doesn’t matter, even if that’s another GS trader. For an illiquid currency, GS may not have sufficient inventory internally. Even if GS has inventory under trader Tom, Tom may not want to Sell the inventory at the market rate at this time. Client ought to get the market rate always.

After the FX trade, GS house account is long USDJPY at price 100 and GS want USD to strengthen. If GS effectively passes on the FX risk, then CK would be long USDJPY.

I believe GS need to Sell USDJPY to CK at price 100, to effectively and completely transfer the FX risk to client. In a nutshell, GS sells 10 greenbacks to CK and CK uses the 10 greenbacks to enter an eq-swap deal with GS.

GS trade system probably executes two FX trades

  1. buy USDJPY on street
  2. sell USDJPY to CK

After that,

  • GS is square USDJPY.
  • CK is Long USDJPY at price 100. In other words, CK wants USD to strengthen.

I believe the FX rate used in this trade must be communicated to CK.

Eleven months later, GS hedge account has $0 PnL since GE hasn’t moved. GS FX account is square. In contrast, CK suffers a paper loss due to FX, since USD has weakened.

As a validation (as I instructed my son), notice that this outcome is identical to the traditional trade, where CK buys USDJPY at 100 to pay for the stock. Therefore, this deal is fair deal.

Q: Does GS make any money on the FX?
A: I don’t think so. If they do, it’s Not by design. By design, GS ought to Sell USDJPY to client at fair market price. “Fair” implies that GS could only earn bid/ask spread.

##[11] data feed to FX pricer #pre/post trade, mid/short term

(see blog on influences on FX rates)

Pricing is at heart of FX trading. It’s precisely due to the different pricing decisions of various players that speculation opportunities exist. There are pricing needs in pre/post trade, and pricing timeframes of long term or short term

For mark to market and unrealized PnL, real time market trade/quote prices are probably best, since FX is an extremely liquid and transparent market, except the NDF markets.

That’s post trade pricer. For the rest of this write-up let’s focus on pre-trade pricer of term instruments. Incoming quotes from major electronic markets are an obvious data source, but for less liquid products you need a way to independently derive a fair value, as the market might be overpriced or underpriced.

For a market maker or dealer bank responding to RFQ,
– IRS, bond data from Bloomberg
– yield spread between government bonds of the 2 countries. Prime example – 2-year Bund vs T-note
– Libor, government bond yield. See http://www.investopedia.com/articles/forex/08/forex-concepts.asp#axzz1SzK7LbkS
– Depth of market
– volume of _limit_orders_ and trades (It’s possible to detect trends and patterns)
– dealer’s own inventory of each currency
– cftc COT report. See http://www.investopedia.com/articles/forex/05/COTreport.asp#axzz1SzK7LbkS
– risk reversal data on FXCM. See http://olesiafx.com/Kathy-Lien-Day-Trading-The-Currency-Market/Fundamental-Trading-Strategy-Risk-Reversals.html

For short term trading, interest rate is the most important input to FX forward pricing — There’s a separate blog post. Other significant drivers must be selected and re-selected from the following pool of drivers periodically, since one set of drivers may work for a few days and become *obsolete*, to be replaced  by another set of drivers.
– yield spread
– T yields of 3 month, 2 year and 10 year
– Libor and ED futures
– price of oil (usually quoted in USD). Oil up, USD down.
– price of gold

For a buy-and-hold trader interested in multi-hear long term “fair value”, pricers need
– balance of trade?
– inflation forecast?
– GDP forecast?

IRS trading system@@ – Eric of Citi

IRS is not transferable. IRS contract can be re-assigned in some cases, but the original 2 counter parties and the new party must all agree.

Both parties must scrutinize the other’s credit worthiness. Libor rate is for top-credit borrowers. If the floating-payer is lower, then the spread on Libor (or the fixed rate?) will reflect that – a.k.a. credit spread. Alternatively, the counter party (floating receiver) can demand collateral.

There’s no secondary market for IRS like there are in listed securities.

Q: Is there an IRS trading system?
%%A: Most needed system might be a deal management system that tracks all our unexpired IRS contracts. Since each deal is bespoke, volume is not high. The basic entity in the system is known not as a position, but a deal. It’s treated like a trade as there are 2 accounts involved, and multiple settlement dates.

Q: Is IRS market regulated?
A: Regulators set limits on total exposure. Participant’s quarterly balance sheets include these IR swaps. One big swap could push a company above the limit.

relative funding advantage paradox by Jeff

(Adapted from Jeff’s lecture notes. [[hull]] P156 example is similar.)
Primary Market Financing available to borrowers AA and BB are
fixed rate
<= AA’s real advantage
floating rate
Libor + 1%
Libor 1.24%
needs to borrow
Note BB has lower credit rating and therefore higher fixed/floating interest costs. AA’s real, bigger advantage is “fixed”, BUT prefers floating. This mismatch is the key and presents a golden opportunity.
Paradoxically, regardless of L being 5% or 10% or whatever, AA and BB can both save cost by entering an IRS.
To make things concrete, suppose each needs to borrow $100K for 12M. AA prefers a to break it into 4 x 3M loans. We forecast L in the near future around  6 ~ 6.5%.
— The strategy –
BB to pay 6.15% to, and receive Libor from, AA. So in this IRS, AA is floating payer.
Meanwhile, AA to borrow from Market fixed 7% (i.e. $7k interest) <= AA's advantage
Meanwhile, BB  to borrow from market L + 1.24% (i.e. L+1.25K) <= BB's advantage
To see the rationale, it’s more natural to add up the net INflow —
AA: -L+6.15  -7 = -L-0.85. This is a saving of 15bps
BB:   L -6.15  -L-1.24 = -7.39. This is a saving of 11bps
Net net, AA pays floating (L+0.85%) and BB pays fixed (7.39%) as desired.
Notice in both markets AA enjoys preferential treatment, but the 2 “gaps” are different by 26 bps i.e. 50 (fixed) ~ 24 (floating). AA and BB Combined savings = 26 bps is exactly the difference between the gaps. This 26 bps combined saving is now shared between AA and BB.
Fake [1] Modified example
fixed rate
floating rate
Libor + 1%
Libor 1.74%
<= AA’s real advantage
needs to borrow
— The strategy –
AA to pay 5.85% to and receive Libor from BB.
Meanwhile, BB  to borrow fixed 7.5% 
Meanwhile, AA to borrow L + 1% <= AA's advantage
Net inflow:
AA:  L -5.85 -L-1 = -6.85, saving 15 bps
BB: -L+5.85-7.5 = -L-1.65, saving 9 bps

[1] [[Hull]] P156 points out that the credit spread (AA – BB) reflects more in the fixed rate than the floating rate, so usually, AA’s advantage is in fixed. Therefore this modified example is fake.

The pattern? Re-frame the funding challenge — “2 companies must have different funding needs and gang up to borrow $100K fixed and $100k floating total, but only one half of it using AA’s preferential rates. The other half must use BB’s inferior rates.
In the 2nd example, since AA’s advantage lies _more_ in floating market, AA’s floating rate is utilized. BB’s smaller disadvantage in fixed is accepted.
It matter less who prefers fixed since it’s “internal” between AA and BB like 2 sisters. In this case, since AA prefers something (fixed) other than its real advantage (float), AA swaps them “in the family”. If AA were to prefer floating i.e. matching her real advantage, then no swap needed.
Q: Why does AA need BB?
A: only if AA needs something other than its real advantage. Without BB, AA must borrow at its lower advantage (in “fixed” rate market), wasting its real advantage in floating market.

trade bust by exchange^swap-dealer

Trade bust is rare on real exchanges, usually for some extreme scenarios.

It’s more common in a equity swap dealer system than an agency broker system. Assuming a buy, there are two transactions:

  1. client leg: contract between dealer and client, client buying IBM from dealer
  2. exchange leg: regular buy on nyse.

After a swap trade is executed i.e. after the hedge order has been executed on nyse, the dealer can bust the client leg. So for the time being there’s only the hedge position on the dealer’s book — risky. Now dealer will execute another client leg transaction at a new price.

fwd contract often has negative value, briefly

An option “paper” is a right but not an obligation, so its holder has no obligation, so this paper is always worth a non-negative value.

if the option holder forgets it, she could get automatically exercised or receive the cash-settlement income. No one would go after her.

In contrast, an obligation requires you to fulfill your duty.

A fwd contract to buy some asset (say oil) is an obligation, so the pre-maturity value can be negative or positive. Example – a contract to “buy oil at $3333” but now the price is below $50. Who wants this obligation? This paper is a liability not an asset, so its value is negative.

Probability of default ^ bond rating

* 1-Y Probability of default (denoted PD) is defined for a single issuer. * Rating (like AA) is defined for one bond among many by the same issuer.

Jon Frye confirmed that an AA rating is not an expression of the firm’s status/viability/strength/health.

I guess the rating does convey something about the LossGivenDefault, another attributes of the bond not the issuer.

CIP ^ UIP, based on Mark Hendricks notes

Without loss of generality, Let’s suppose the loan period is “today + 12M”.

CIP (not UIP) is enforced by arbitrage and proven by real data. UIP is kind of naive theory, inconsistent with real data.

CIP relates 4 currently observed prices including a fwd exchange rate 12M forward (something like a rate lock). See http://bigblog.tanbin.com/2012/08/fx-fwd-arbitrage-4-ba-spreads-to.html

UIP relates 3 currently observed prices + a yet-unknown price —

E[spot rate 12M later] ) / spot rate = IntRate1/IntRrate2

Above expectation is in _physical_ measure i.e. wishful thinking (IMHO). CIP replaces that expectation with the risk-neutral E*[spot rate 12M later] := fwd contract price today.

RN basically means “backing out the forward contract’s valuation using live market data”. This back-out price is enforced by CIP arbitrage.

CIP arbitrage involves 4 trades done simultaneously. UIP can also involve several trades, but one of them is executed _12_M_ later, so the execution price is unknown now and could lose money.

equivalent FX(+option) trades, succinctly

The equivalence among FX trades can be confusing to some. I feel there are only 2 common scenarios:

1) Buying usdjpy is equivalent to selling jpyusd.
2) Buying usdjpy call is equivalent to Buying jpyusd put.

However, Buying a fx option is never equivalent to Selling an fx option. The seller wants (implied) vol to drop, whereas the buyer wants it to increase.

BUY a (low) interest rate == Borrow at a lock-in rate

Q: What does “buying at 2% interest rate” mean?

It’s good to get an intuitive and memorable short explanation.

Rule — Buying a 2% interest rate means borrowing at 2%.

Rule — there’s always a repayment period.

Rule — the 2% is a fixed rate not a floating rate. In a way, whenever you buy you buy with a fixed price. You could buy the “floating stream” …. but let’s not digress.

Real, personal, example — I “bought” my first mortgage at 1.18% for first year, locking in a low rate before it went up.

factors affecting bond sensitivity to IR

In this context, we are concerned with the current market value (eg a $9bn bond) and how this holding may devalue due to Rising interest rate for that particular maturity.

* lower (zero) coupon bonds are more sensitive. More of the cash flow occurs in the distant future, therefore subject to more discounting.

* longer bonds are more sensitive. More of the cashflow is “pushed” to the distant future.

* lower yield bonds are more sensitive. On the Price/yield curve, at the left side, the curve is steeper.

(I read the above on a slide by Investment Analytics.)

Note if we hold the bond to maturity, then the dollar value received on maturity is completely deterministic i.e. known in advance, so why worry about “sensitivity”? There are 3 issues with this strategy:

1) if in the interim my bond’s MV drops badly, then this asset offers poor liquidity. I won’t have the flexibility to get contingency cash out of this asset.

1b) Let’s ignore credit risk in the bond itself. If this is a huge position (like $9bn) in the portfolio of a big organization (even for a sovereign fund), a MV drop could threaten the organization’s balance sheet, credit rating and borrowing cost. Put yourself in the shoes of a creditor. Fundamentally, the market and the creditors need to be assured that this borrower could safely liquidity part of this bond asset to meet contingent obligations.

Imagine Citi is a creditor to MTA, and MTA holds a bond. Fundamental risk to the creditor (Citi) — the borrower (MTA)  i.e. the bond holder could become insolvent before bond maturity, when the bond price recovers.

2) over a long horizon like 30Y, that fixed dollar amount may suffer unexpected inflation (devaluation). I feel this issue tends to affect any long-horizon investment.

3) if in the near future interest rises sharply (hurting my MV), that means there are better ways to invest my $9bn.

FX vol quoting convention

? the terms “strangle” and “butterfly” seem to be used rather loosely. Not sure which is actually right. Do they mean the same thing?

On the fx vol dealer market, you get quotes in the form of RiskReversal, Strangle and ATM straddle.
An example of a RR quote is a 25 delta RR contract to convert 1 million USD to JPY. The exact sums of yens are denoted Kp25 and Kc25, and not in the quote. In this kind of confusing discussions, just treat the commodity currency (USD in this case) as a commodity like silver. When you (market-Taker) go Long any RR contract, you are Long the Call and Short the Put on that silver – Be very clear about these in your mind.
Now let’s zoom into a hypothetical RR quote. The quote says
“            On Mar 1, dealer UBS is willing to WRITE a USD call + BUY a USD put for a premium amount of x yens[1], where x will be determined at the RR volatility of 3.521% per annum. (An unrealistic fictitious vol value, because USD/JPY RR quote is usually Negative.)
The underlying Put has a strike Kp25 corresponding to a delta of -0.25. (But since you the market Taker will be Short the Put, your delta is +0.25.)
The underlying Call has a strike Kc25 corresponding to a delta of +0.25. This Call strike will be Above the Put strike.
Both the put and the call are OTM for 1 million unit of USD and expire end of May.
Optionally, the quote might mention a reference spot rate of “USD/JPY = 93.32”. This probably helps people back out the strikes Kp25 and Kc25.
That is a one-way Offer/Ask quote. For a 2-way, dealer would give 2 quotes — a bid and an ask.

[1] Note the RR instrument is denominated in yen i.e. yen is the “2nd” currency whereas dollar is the commodity like “silver”

At the time when you accept this quote, Kp25 might come out to be 88 million yens, and Kc25 might come out to be 111 million yens. The premium x might come out to be 2.5 million yens – all hypothetical figures. However, if you accept the quote an hour later, live prices would move, and Kp25, Kc25 and x would be different even if the 3.521% quote stays largely unchanged. FX volatility smile curve is known to be sticky-delta, rather than sticky-strike (stocks).

Lets see how to compute Kp25 from this quote. In the standardized RR contract, the quoted vol of 0.03521 pa is defined as the vol difference i.e. 
sigmaKc25sigmaKp25 = 0.03521 per annum
sigmaKc25 is the implied vol of the underlying call (subcontract) at strike Kc25
sigmaKp25 is the implied vol of the underlying put (subcontract) at strike Kp25
On any FX/Equity smile curve, Kp25 < Kp25, so on the graph the sigmaKc25 (implied vol on the OTM Put) is always marked on the LHS and the Call always on the RHS. For USD/JPY, smile curve looks like a stock, so LHS sigma is Higher than RHS. Therefore the RR vol is usually negative.
To determine the exact Kc25 and Kp25 values, we need to compute the 2 above-mentioned sigmas, which bring us to the Strangle and ATM quotes.
The Strangle quote says something like
“           On Mar 1, dealer UBS is willing to WRITE 2 options — a USD (i.e. silver/JPY) put + WRITE a USD (i.e. silver/JPY) call for a premium amount of x yens, where x will be determined at the volatility level of 5.1% per annum.
The put has a strike Kp25 corresponding to a delta of -0.25.
The call has a strike Kc25 corresponding to a delta of +0.25.
Both the put and the call are OTM for 1 million unit of USD (silver) and expire end of May.
The quoted vol of 0.051 pa is defined as (sigmaKc25 + sigmaKp25) / 2 – sigmaATM = 0.051 per annum
The ATM (straddle) quote says something like
“            On Mar 1, dealer UBS is willing to WRITE a USD (i.e. silver/JPY) call + WRITE a USD (i.e. silver/JPY) put for a premium amount of x yens, where x will be determined at the volatility level of 11% per annum.
The call and the put both have exactly the same strike K such that net delta = 0.0. (This K is not specified in the quote. This K makes both options ATM but K is not exactly equal to current spot rate.)
Both are ATM for 1 million unit of USD (“silver”) and expire end of May.
The quoted 11% vol is the above-mentioned sigmaATM. ATM put and call should have very similar (implied) sigmas. Their delta should both be very close to 0.50.
With these 3 quotes, it’s simple arithmetic to back out the 2 unknown sigmas – the implied vol for the underlying 25-delta OTM call and the underlying 25-delta OTM put. The RR is a portfolio of these 2 primitive instruments. The Strangle is also a combination of these 2 basic instruments. Note the 3 quotes may come from 3 dealers, so as a market taker we can mix and match the available contracts.
If we know the implied vol (sigmaKc25) of a 25-delta OTM call, and also the spot price and expiration, BS can back out the strike price Kc25. Remember there’s a one-to-one math relationship between delta values and strike values. Imagine we have a lot of (3000) call contracts with equally spaced strikes, same expiration. If we plot their Theoretical values against their strikes, we will see a smile curve. Mathematically, their delta values (not defined this way but) are numerically identical to the gradient along this smile curve. If we plot delta against strikes, we will see the one-to-one-mapping.

Gaussian HJM, briefly

… is a subset of HJM models.

An HJM model is Gaussian HJM if vol term is deterministic. Note “vol” term means the coefficient of the dW term. Every Brownian motion must always refer to an implicit measure. In this case, the RN measure.

How about the drift term i.e. the “dt” coefficient? It too has to be deterministic to give us a Gaussian HJM.

Well, Under the RN measure, the drift process is determined completely by the vol process. Both evolve with time, but are considered slow-moving [1] relative to the extremely fast-moving Brownian Motion of “dW”. Extremely because there’s no time-derivative of a BM

[1] I would say “quasi constant”

Language is not yet precise so not ready to publish on recrec…

various discount curves

For each currency

For each Libor tenor i.e. reset frequency like 3M, 6M

There's a yield curve

STIRT traders basically publish these curves via Sprite. Each currency has a bunch of tenor curves + the FX-OIS curve

This is the YC for the AA credit quality. In theory this yield curve is not usable for a different credit quality. For a BB credit quality, the mathematicians would, correctly, assume a yield curve but in reality I doubt there's a separate curve.

In contrast, there is indeed a tenor curve at 1Y, and other tenors too.

Basis swap means interest rate swap between 2 floating “floating streams”.

* swap between 2 currencies

* swap between 2 Libor tenors

* swap between 2 floating indices. These curves below have different credit qualities:

** Libor — AA banks

** OIS — much lower credit risk given the short tenor

** T-bill — US government credit

bonds – relevant across FI models #HJM..

Bonds are no longer the dominant FI instrument, challenged by IRS and futures. However, I feel for Fixed Income models bonds are more important, more useful than any other instrument.

– Bond (unlike swap rates, FRA rates etc) is a tradeable, and obeys many nice martingale pricing rules.

– Zero Bond can be a numeraire.

– For model calibration, zero bond prices are, IMO, more easily observable than swap rates, FRA rates, cap prices, swaption prices etc. I think futures prices could be more “observable” but the maturities available are limited.

– Zero bond’s price is exactly the discount factor, extremely useful in the math. I believe a full stochastic model built with zero bond prices can recover fwd rates, spot rates, short rates, swap rates and all others …

– I believe term structure models could be based on fwd rate or short rate, but they all need to provide an expression for the “zero bond process” i.e. the process that a given bond’s price follows. Note this process must converge to par at maturity.

– Bond as an instrument is closely related to caps and floors and callable bonds.

– Bonds are issued by all types of issuers. Other instruments (like swaps, IR futures) tend to have a smaller scope.

– Bonds are liquid over most regions of the yield curve, except the extreme short end.

fwd price@beach^desert – intuitive

Not that easy to develop an intuitive understanding…

Q2.46 [[Heard on the street]]. Suppose the 2 properties both sell for $1m today. What about delivery in x months? Suppose the beach generates an expected (almost-guaranteed) steady income (rental or dividend) of $200k over this period. Suppose there’s negligible inflation over this (possibly short) period.

Paradox: you may feel after x months, the beach would have a spot price around $1m or higher, since everyone knows it can generate income.
%%A: there’s no assurance about it. It could be much lower. I feel this is counter-intuitive. There might be war, or bad weather, or big change in supply/demand over x months. Our calculation here is based solely on the spot price now and the dividend rate, not on any speculation over price movements.

I guess the fair “indifferent” price both sides would accept is $800k, i.e. in x months, this amount would change hand.
– If seller asks $900k forward, then buyer would prefer spot delivery at $1m, since after paying $1m, she could receive $200k dividends over x months, effectively paying $800k.
– If buyer bids $750k forward, then seller would prefer spot delivery.

What would increase fwd price?
* borrowing interest Cost. For a bond, this is not the interest earned on the bond
* storage Cost

What would decrease fwd price?
* interest accrual Income
* dividend Income

arbitrate-free term structure models

Sound byte — if we have 2 unrelated stochastic processes for 2 points on the YC, the 2 calculated prices can induce arbitrage.

Jargon: whenever you see “process”, always think of “distro” under some “measure”.

Jargon: whenever you see “price”, it almost always means a fair “quote” on some contract whose terminal value is yet to be revealed. This price comes directly from the distro by discounting the expected payoff

Jargon: bond prices basically mean loan rates, possibly forward-start. Libor is a loan. FRA is a loan. ED-future represents a loan. A single-period IR swap consists of 2 loans. OIS is based on overnight loans. I notice that from any term structure model, we always want to back out the PROCESS of various bond prices. I guess that's because the actual contracts are invariably written in terms of loans.

Preliminary: IMO, a simple IR option is a call/put on one point of the YC. Example is a call on the 3M Libor. Libor rate changes every day, so we can model it as a stochastic PROCESS. We can also model the evolution of the entire YC with 20 “points” or infinite points.

Earlier formula used to price IR options (including bond options, caps, swaptions) is not from an IR model at all. Black's formula was proposed for options on commodity futures. When adapted to interest rates, Black's formula was kind of OK to price options on one point on the (evolving) yield curve, but problematic when applied to multiple points on the YC.

As a consequence, such a model can

– give a distribution of an (yet unrevealed) discount factor of maturity M1, after calibrating the model params with one set of market data

– give a distribution of an (yet unrevealed) discount factor of maturity M2, after calibrating the model params with another, unrelated set of market data

As a result, the 2 distributions are like the speculations by 2 competing analysts — can be contracting. If a bank uses such a model, and gives quotes based on these 2 distros, the quotes can be self-contradicting, i.e. inducing arbitrage. I would imagine the longer-maturity yield (converted from the discount factor) could turn out to be much lower than short-maturity, or the yield curve could have camel humps.

Following Black's formula, First generation of IR models describe the short rate evolution as a stochastic process, but short rate can't “reproduce” a family photo. In other words, we can't back out the discount factor of every arbitrary maturity.

More precisely, given a target date “t” [1] the model gives the distribution of the (unrevealed) short rate on that target date, but the zero-curve on that target date has infinite points, each being a discount factor from some distant future (like 30Y) to the target date. The short rate distribution is not enough to reproduce the entire YC i.e. the family photo.

The only way I know to give consistent [2] predictions on all points of the YC is a model describing the entire YC's evolution. We have to model the (stochastic) process followed by any arbitrary point on the YC, i.e. any member on the family photo. The model params thus calibrated would be self-consistent.

[1] that's later than the last “revelation” date or valuation date, i.e. any IR rate on the target date is unknown and should have some probability distribution.

[2] arb-free, not self-contradicting

Sound byte — disconnected, unrelated Processes for 2 bonds (eg 29Y vs 30Y) could induce arbitrage. These 2 securities are unlike Toyota vs Facebook stocks. I think the longer maturity bond can be used to arbitrage the shorter maturity. I think it's safe to assume non-negative interest rate. Suppose both have face value $1. Suppose I could buy the long bond at a dirt cheap $0.01 and short-sell the short bond at a high $0.98 and put away the realized profit…..

option delta hedge – local anesthesia#RogerLee…

An intuitive explanation given by Roger, who pointed out that delta hedge insulates you from only small changes in stock (or another underlier).

Say, you use 50 shares to hedge an ATM option position with delta hedge ratio = 50%. Suppose your hedge is not dynamic so you don’t adjust the hedge, until price moves so much the option delta becomes close to 100%. Now a $1 move in your option is offset by $0.50 change in the stock position – insufficient hedge.

The other scenario Roger didn’t mention is, the option becomes deeply OTM, so delta becomes 1%. Now a $0.01 change in your option position is offset by $0.50 of the stock position – overhedged.

ED-fut to replicate IRS

I feel FRA is the correct thing to replicate IRS…

The LTCM case P13 footnote very briefly described how to replicate IRS using ED futures.

Say we have a vanilla 10Y IRS based on 3M Libor. There are 40 payments, either incoming or outgoing. First payment is 3M after trade date (assuming Jan 1), when BBA announces the 3M Libor for Apr-Jun. Based on the differential against the pre-agreed fixed rate, one party will pay the other.

Here’s how an ED trader replicates this IRS position — On trade date she would simultaneously buy 40 (or sell 40) futures contracts each with a maturity matching those announcement dates.

In both cases, we are sensitive to all the 40 Libor rates to be announced. Each rate is a 3M spot deposit rate.

delta neutral strike FXO, briefly

d1 = 0

Therefore, |put delta| = call delta = N(d1) = 0.5

According to Fang Chao:
call delta = N(d1)
put delta = 1 – N(d1)

Q: is it always true that |put delta| + call delta = 1?
A: I think so, if without dividend. See http://en.wikipedia.org/wiki/Greeks_(finance)#Relationship_between_call_and_put_delta

earning/paying the "roll" in FX swap

Tony gave an example of sell/buy NZDUSD.    NZD is high yielder and kind of inflationary. Therefore, far rate is Lower. We sell high buy low, thereby Earning the swap points.

Buy/Sell USDJPY is another example. USD is high yield, and inflationary, so far rate is Lower. We buy high, sell low, therefore paying the swap points.

paradox – FX homework#thanks to Brett Zhang

label – math intuitive


Q7) An investor is long a USD put / JPY call struck at 110.00 with a notional of USD 100 million. The current spot rate is 95.00. The investor decides to sell the option to a dealer, a US-based bank, on day before maturity. What is the FX delta hedge the dealer must put on against this option?

a) Buy USD 100 million

b) Buy USD 116 million

c) Buy USD 105 million

d) Buy USD 110 million


Analysis: The dealer has the USD-put JPY-call. Suppose the dealer has USD 100M. Let’s see if a 1 pip change will give the (desired) $0 effect.


at 95.00

at 95.01, after the 1 pip change


value (in yen) of the option is same as value of a cash position

(110-95)x 100M = ¥1,500M

(110-95.01) x 100M = ¥1,499M

loss of ¥1M

value (in yen) of the USD cash

95 x 100M = ¥9,500M

95.01 x 100M = ¥9,501M

gain of ¥1M

value of Portfolio




Therefore Answer a) seems to work well.


Next, look at it another way. The dealer has the USD-put JPY-call struck at JPYUSD=0.0090909. Suppose the dealer is short 11,000M yen (same as long USD 115.789M). Let’s see if a 1 pip change will give the (desired) $0 effect.


at 95.00 i.e. JPYUSD=0.010526

at 95.01 i.e. JPYUSD=0.0105252, after the 1 pip change


value (in USD) of the option is

same as value of a cash position

(0.010526-0.009090)*11000M =

$15.78947M (or ¥1500M, same as table above)


$15.77729M (or ¥1498.842M)

loss of $0.012187M


value (in USD) of the short

11,000M JPY position

-0.010526 * 11000M= -$115.789M

-0.0105252*11000M = -$115.777M


gain of

$0.012187M (or ¥1.1578M)

value of Portfolio




Therefore Answer b) seems to work well.


My explanation of the paradox – the deep ITM option on the last day acts like a cash position, but the position size differs depending on your perspective. To make things obvious, suppose the strike is set at 700 (rather than 110).

1) The USD-based dealer sees a (gigantic) ¥70,000M cash position;

2) the JPY-based dealer sees a $100M cash position, but each “super” dollar here is worth not 95 yen, but 700 yen!


Therefore, for deep ITM positions like this, only ONE of the perspectives makes sense – I would pick the bigger notional, since the lower notional needs to “upsized” due to the depth of ITM.


From: Brett Zhang

Sent: Monday, April 27, 2015 10:54 AM
To: Bin TAN (Victor)
Subject: Re: delta hedging – Hw4 Q7


You need to understand which currency you need to hold to hedge..


First note that the option is so deeply in the money it is essentially a forward contract, meaning its delta is very close to -1 (with a minus sign since the option is a put). It may have been tempting to answer a), but USD 100 million would be a proper hedge from a JPY-based viewpoint, not the USD-based viewpoint. (Remember that option and forward payoffs are not linear when seen from the foreign currency viewpoint.)


To understand the USD-based viewpoint we could express the option in terms of JPYUSD rates. The option is a JPY call USD put with JPY notional of JPY 11,000 million. As observed before it is deeply in the money, so delta is close to 1 (positive now since the option is a call). The appropriate delta hedge would be selling JPY 11,000 million. Using the spot rate, this would be buying USD 11,000/95 million = USD 116 million. 


On Sat, Apr 25, 2015 at 2:21 AM, Bin TAN (Victor) wrote:

Hi Brett,

Delta hedging means holding a smaller quantity of the underlier, smaller than the notional amount, never higher than the notional.

This question has 4 answers all bigger than notional?!



fwd-starting fx swap points

Q: If 9M outright fwd point is 15.2 pips, and 3M is 5 pips, what would be the fwd-starting swap point?

A (not sure now): The swap point would be 15.2 – 5 = 10.2 pips.

The fwd point for a 3Mo (our near date) is F – S = S (1 + R * 90/360)/(1 + r * 90/360) – S, which already considers the 3Mo length.

This formula shows the
* near date fwd point number is linear with (R – r).
* far date fwd point number is linear with (R – r).

However, the linear factors in these 2 cases are Different so it’s wrong (??) to subtract like 12 – 5 basis points. Swap point reflects not only the IR differential, but also the “distance” and the spot level.

The swap points are smaller when the distance is short.

Suppose you as market taker have an existing 3M fwd position and need to roll it forward. You effectively need to close the position for the original maturity and redo it at 9M. That’s 2 transactions with 2 dealers — unwise. Instead, You should go to one dealer to get a fwd-starting swap quote in bid/ask, without revealing your direction. The dealer would charge bid/ask only on the far leg, not twice on near leg and far leg.
Specifically, If there’s a bid/ask on the 3M fwd point (5 pips for eg), that doesn’t increase the swap point bid/ask spread, which would be the same bid/ask spread as the far leg fwd points.

x-ccy basis swap – FX homework3 revelations

For x-ccy fixed/fixed IRS, There are 2 levels of learning
11) the basic cash flows; how this differs from IRS and FX swap …This proves to be more confusing than expected, and harder to get right. Need full-blown examples like course handout from Trac consultant. It’s frustrating to re-learn this over and over. May need to work out an example or self-quiz.
22) the underlying link to x-ccy basis swap
A1b: Either issue EUR fixed bond or USD fixed then somehow swap to EUR
A1: fixed USD
A4: euro. Yes. They can simply convert the USD fund raised, in a detachable spot transaction. This is fully detachable so not part of the currency swap at all.
A9: 0 point. Rate is the trade date spot
A2 no

11) Self-quiz on the Trac illustration, to go thin->thick->thin and develop intuition.
Q1: before the deal, is Microsoft already an issuer of fixed or floating bond? What currency?
Q1b: Before issuing any debt whatsoever, what are Microsoft’s funding choices?
Q2: Is there any principal exchanged on near date (i.e. shortly after trade date)?
Q3: Microsoft is immune to FX movement or USD rate movement or EUR rate movement? What is Microsoft betting on?
Q4: Microsoft needs funding in what currency? Are they getting that from the deal?
Q9 (confusing): how is this diff from FX swap? How is swap point calculated?

My mistake in this homework was forgetting that the far-date FX rate used to exchange the principal amount is the rate pre-determined on trade date, written into the contract, and not subject to FX movement up thereafter.

22) I now think the x-ccy basis swap spread is important to any x-ccy IRS aka “currency swap”, because a x-ccy basis swap is an implicit part and parcel of it….

http://quantfather.com/messageview.cfm?catid=8&threadid=75575 points that usd/aud [1] basis swap of 15 bp is interpreted as

“usd libor flat -vs- aud default floating rate + 15 bp, with tenor basis spread adjusted [2].”

[1] or aud/usd…. It doesn’t matter.
[2] in aud case, the default swap coupon tenor is same as USD and needs no adjustment

I guess the spread is positive because aud is a high yielder? Not sure

–The coca cola bond in http://www.reuters.com/article/2015/02/27/coca-cola-bonds-idUSL5N0W127E20150227
US issuers (needing usd eventually) of eur floating bonds [3] would use x-ccy basis swap to convert the euribor liability to a “usd libor + 33” liability, so the negative and growing spread (-33 now) hurts.

Warning — it’s incorrect to think “ok for this quarter my euribor liability is 2% for this quarter, so 2% – 33 bps = 1.67% and I swap it to a usd libor liability, so the bigger that negative spread, the lower my usd libor liability — great!” Wrong. The meaning of -33 is

“paying euribor floating rate (2% this quarter), I can find market makers to help me convert it into paying a usd libor+33”
“paying 2% – 33 bps on a euribor floating bond, I can convert it into paying a usd libor + 0 floating bond”

[3] fixed bond can be swapped to floating
http://www.global-derivatives.com/forum/index.php?topic=444.0;wap2 explains
There is more demand for funding in one currency and more supply in another currency. For instance many Japanese banks have funding sources in JPY but have committments in USD. They therefore will swap their JPY (inflow) to USD (inflow) to cover their USD commitments. The basis swap spread reflects this supply and demand situation.

Assuming a tiny bid/ask spread, I believe a Japanese bank is equally willing to receive
– a stream of usd libor or
– a stream of jpy libor – 10 bps

By the no-arbitrage pricing principle, two floating rates should trade at par and the basis spread should be zero (Tony also covered this point in the 3rd lecture), but there’s more demand for usd libor inflow.

Similarly, after GFC, European banks need usd more than US banks need euro. see http://www.business.uwa.edu.au/__data/assets/pdf_file/0008/2198339/Chang-Yang-UTS.pdf. A typical bank would be indifferent to receiving
– a stream of usd libor or
– a stream of euribor – 34 bp

https://doc.research-and-analytics.csfb.com/docView?language=ENG&format=PDF&source_id=csplusresearchcp&document_id=1014795411&serialid=mW557HA4UbeT5Mrww553YSwfqEwZsxUA4zqNSkp5JUg%3D explains that

the basis swap markets saw increased demand to receive USD funds in exchange for EUR. This excess demand drove the EURUSD basis swap spreads down to highly negative levels as counterparties were willing to receive lower interest payments in return for US dollar funds

eq-fwd contract – delivery price K

Eg: me buying Blk 155 flat. In Oct we agreed on $615 delivery price. Cash-On-Delivery on the delivery date in Feb. “Logistics”… No exposure no mkt risk.

Eg from [[hull]] P104. $40.50 delivery price means $40.50 cash to change hand on the delivery date.

Simple rule — No cash flow on execution date – different from most other trades. Simple difference yet very confusing to some.

Simple rule — To understanding the “delay”, we can imagine sky high interest, carry and inflation rates.

Simple rule – Cash-On-Delivery

I feel the delayed cashflow is at the heart of the (simple) arb and math. If we aren’t absolutely clear about this delay, big messy confusions …

EE context — yes deliver price is an important factor to PnL, risk mgmt etc
QQ context – delivery price is the price quoted and negotiated

Q: In each fwd contract, are there 2 prices?
QQ context – 1 only
EE context – 2 indeed. Similar to simply buying then holding IBM shares. Both prices are relevant in the EE context —
• K is the negotiated “execution” price, implicitly written into the fwd contract
• there’s a live market price for the same fwd contract.

swaps illustration diagrams — how to read

This write-up covers IRS, x-ccy swap…

These block diagrams are popular and partially useful, but beginners often don't realize:

* initial context — typically a corporation has a periodic liability, or an investor has a periodic income.

** We had better ignore all the other arrows first.

* the motivation — typically to convert the initial single arrow to other arrows. The swap contract adds 2 arrows, one of them cancelling out the pre-existing arrow.

** we had better focus on the 3 arrows and ignore other parts of the diagram.

yield curve , according to Jeff

Jeff’s lecture notes (in 0xpdf) has detailed explanations on

1) EUR OIS YC bootstrapping using specific OIS instruments
2) Libor YC under OIS discounting — so OIS curve + libor curve needed.
3) Libor curve for a non-default tenor, such as 6M or 2M

lots of “root-finding”… but not too hard.

A YC (or a term structure) can be represented as a series of
* spot disc factors
* fwd disc factors
* spot interest rates
* fwd interest rates

Rebanato – good author on fixed income models

recommended by Sian Hwee.

Ronnie said Black model is popular (largely due to simplicity, and historical reason), and many option products are quoted in terms of vols implied from the Black model. 
TA seems to agree that the advanced models (beyond the Black model) are still needed but indeed harder than the earlier lectures before the Black model.

buying (i.e. long) a given interest rate

Tony (FX lecturer) pointed out “buying” any variable means executing at the current “level” and hope the “level” moves up. (Note a mathematician would point out an interest rate is not directly tradeable, but never mind.)

Therefore, buying an interest rate means borrowing (not lending) at a rock bottom rate.
Wrong intuition — “locking in the interest income stream”.
Eg: Say gov bond interest is super low, we would borrow now, and hope for a rise.
Eg: Say swap rate is super low, we would lock it in — pay fixed and lock in the floating income stream, and hope for the swap rate and floating stream both to rise.

bid side of fx swap point means@@

Q: given a pair of bid/ask quotes in fx swap point, what kind of trades are we talking about implicitly?

A: dealer is sell/Buy ccy1. The spot leg is sell ccy1. The far leg is Buy ccy1.

Note we are taking the dealer’s position, not the market-taker’s.

Note “bid” refers to the far leg, not the near leg.

Note ccy1 (not ccy2) is the asset being traded.

par swap rate drop means …@@

For a given tenor (say 1Y)


I think treasury yield rise (or drop) has a simpler interpretation….


I think Libor ED deposit rate drop (or rise) has another simple interpretation …. and has a credit element.


Libor par swap rate drop has a non-trivial interpretation….


OIS swap rate is even more complicated…

OIS fund.rate – which side pay xq@collateral#eg IRS

I think whoever accepting/receiving/holding the collateral would pay interest on the collateral. I think the same guy can also lend it out, perhaps overnight. Similar to a bank holding your deposit…

Consider cash collateral for simplicity…

The original owner of the collateral could earn a daily interest if deposited in a bank. When she pledges it as collateral, she is still entitled to the same interest income. Someone has to pay that interest.

Now consider a MBS or a bond. They all generate a periodic income, just like cash collateral.

FRA^ED-fut, another baby step

I think the differences like convexity adjustment are not “sticky” in my memory, after I tried many times to internalize, so no thin->thick->thin…

Jeff (MSFM) pointed out

* FRA — on expiry date you know the settlement amount. 2 days later that amount physically settles. That’s the accrual period start date!
* ED futures – every day you give or take a bit of the (usually big) settlement amount. On IMM date full amount settles. No 2-day delay.
ED has Neg convexity versus FRA, so whether your realized pnl is P or L, FRA is a bit “better” (for the holder) than ED for the same strike.

bonds let us to lock in a profit today to be realized in N years

After my lecturer touched on this point, I did some research.

For equities, say IBM, if we buy it at $100 and hope to cash out about
5 years from now, we are never confident. At that time, price could
drop below $100 and we may have to wait indefinitely to recover our
capital. That’s the nature of equity investment. Barring another
financial crisis (which i consider unlikely in the next 20 years),
price should recover but I might have bought at the peak, as I did
many times in my experience.

For a bond with a coupon rate 7.5% per year, maturing in 5 years, the
current price could be about $100, which translates to a yield around
7.5%, probably a high yield bond issued by some lesser-known entity
XYZ. If all the coupons are paid out only on maturity without
compounding, then the yield turns to be around 6.5%, as illustrated in
the attached spreadsheet.

The special thing about bond (relative to stocks) is, we kind of lock
in an annualized return of 6.5% at the time we buy it, barring credit

As the attached spreadsheet illustrates, today we pay about $100 to
own the bond, and in 60 months we are sure to receive exactly $137.5
i.e. $7.5 x 5 years coupon payment. This terminal value is not subject
to any market movement. The only uncertainty is credit default. Most
bonds we deal with, even the high yield bonds, are very unlikely to
default. If you buy a bond fund, then you would invest into hundreds
of bonds, so some defaults may be compensated by other bonds’ positive

If you don’t want to worry about defaults at all, then get a
investment grade bond, perhaps at a yield of 4%. You still lock in
that annualized 4% if you hold it till maturity.

The spreadsheet shows that even if there’s a credit crunch some time
before maturity, the bond’s market value (NAV) may drop drastically,
but it is sure to recover. Even if yield goes up in the last year,
barring default, the maturity value is still exactly $137.5. This
guaranteed return is something stocks can’t offer.

There are other factors to muddy the water a bit, but the simple fact
is, barring default, we could effectively lock in a profit today, to
be realized on the bond’s maturity date.

I guess that’s how insurers can guarantee returns over many decades.
They buy very long bonds which offer higher yields.

What do you think?

FX, short term rate, YC…again

(labels – fixedIncome, original_content, z_bold)

I feel FX market mostly watch short term rates, not long term rates. Short-term typically means below 1 year.

– long term IR Futures are based on government debt + … other factors. Examples — T-futures, German Bund futures,…
– short term IR is usually based on OIS, Libor or similar inter-bank offer rates in other cities like Tokyo, Singapore, Hongkong …

Short term (including O/N) borrowing is probably more prevalent than long term borrowing. Credit risk grows significantly with the borrowing duration.

Yield Curve and Swap Curve are directly comparable. Yield curve is about spot Interest Rate. Swap curve is also about spot IR !! although swap curve is constructed using mostly forward Interest rates — only the first few (3) months of the curve data points are constructed using spot IR rates

* Conceptually, you can imagine we convert either spot IR or fwd IR to discount factors at various valuation dates.
** we could get a DF from 2040 to 2030.
** we could get a DF from 2042 to today.

From a discount curve, we can “back out” the spot rates for various tenors. A spot rate is directly related to a DF to today.

* Libor itself is a spot lending rate but Libor Futures and Libor swap contracts are about Forward lending rates — Very important

-ve fwd points => ccy1 weakening => ccy1 higher inflation

(As we get older we rely increasingly on intuition, less on memorizing)

Tony shared this quick intuition :
* when we see a …negative fwd point, we know ccy1 is …weakening due to … higher inflation in that country, such as AUD or BRL
* when we see a positive fwd point, we know ccy1 is strengthening due to ultra-low inflation such as EUR.

(Note the lowest inflation currency, JPY, is never a first currency…)

Remember ccy1ccy2 = 108.21 indicates the “strength of cc1”

– When we see ccy1 IR lower than ccy2, we know ccy1 will likely strengthen in the short term. You can imagine hyper-inflation in ccy2
– When we see ccy1 IR higher than ccy2, we know ccy1 will likely weaken in the short term. You can imagine hyper-inflation in ccy1

option math : thin -> thick -> thin

Many topics I may have to give up for lack of bandwidth. For the rest of the topics, let’s try to grow the “book” from thin to thick then to thin.



+ delta hedging

+ graphs of greeks

+ arbitrage constraints on prices of European calls, puts etc. Intuition to be developed

+ basic strategies like straddle                     


LG American options


LG binary options but ..

+ Roger’s summary on N(d1) and N(d2)

LG div

LG most of the stoch calc math but ..

LG vol surface models

+ some of the IV questions on martingale and BM


PRICE is clean or dirty;YIELD is always "dirty"

Traders quote clean price. However, Full price, Dirty price, or Invoice price is the price used for settlement.

YTM is neither clean or dirty. YTM is always “converted” from dirty price. My lecturer said —

There is only one yield to maturity.  It is neither of a “clean” nor “invoice” type.  The formula relating yield to maturity to bond price refers to the invoice price, not the clean price. 

bond "callable" provision is a risk to investor#my take

see also post on price spread between callable and non-callable bonds

To a buyer of a callable bond, the call feature poses a “call risk”.

Q: Why is early repayment a risk to the lender? To me it sounds like an added value.
A: The issuer only exercises this option when advantageous. Advantageous to issuer always means bad luck for the counter-party i.e. bond holders.

Bond is called only in a low-interest period. Imagine you receive 10% pa coupons year after year and suddenly you get the principal back but you can get only 0.0% pa (like Japan or Europe) from now on 😦

When an investor is comparing 2 otherwise identical bonds, the one with the call option is worth less because there’s a risk (“call risk”) that cash-flow will be lower after the call option exercise.

Yield-to-worst is basically the lowest yield that could be realized if the embedded call is exercised. Buyer assumes what could go wrong WILL go wrong — Murphy’s Law. In such an analysis, the worst case to the investor is an early repayment, and reduced cash-flow subsequently.

However, my friend Ross (in the bubble room) in Macquarie said the callable bond they hold could get called and as a result they could realize a windfall profit. He said it’s a good thing but I believe they would forgo the high coupon interest.

bond "callable" provision is a risk to investor#CFA textbook

See also post on why a bond’s callable provision is a risk.

P260 of CFA textbook on Eq and FI has a concise explanation.

– Suppose A issues a riskless non-callable bond, for a $109 price.
– Suppose B issues a callable bond, with identical features otherwise, for $106.8 price. The $2.2 price difference is the value of the embedded call option (to the issuer).

If issuer A uses $2.2 of the sales proceeds to buy a call option (to receive the coupons), then A’s position would match B’s. When rates drop to a certain level, the B issuer would call the bond, ending her obligation to pay those high coupons. A would continue to pay coupons, but his call option would produce a cash flow matching the coupon obligations.

Notice the callable bond is cheaper because the issuer holds a call option — to be exercised if low-interest happens.

Also notice — as expected IR volatility (implied vol) rises, the embedded option is worth more and the price spread between the A vs B bonds will widen.

In fact, since A price isn’t sensitive to vol, B price must drop — intuitive?

The B issuer is (believed to be) more likely to call the bond and refinance at a lower coupon, whereas the A bond will continue to pay the super-high coupon until maturity. So bond A is more valuable to an investor.

intuitive – dynamic delta hedging

Q: Say you are short put in IBM. As underlier falls substantially, should you Buy or Sell the stock to keep perfectly hedged?

As underlier drops, short Put is More like long stock, so your short put is now more “long” IBM, so you should Sell IBM.

Mathematically, your short put is now providing additional positive delta. You need negative delta for balance, so you Sell IBM. Balance means zero net delta or “delta-neutral”

Let’s try a similar example…

Q: Say you are short call. As underlier sinks, should you buy or sell to keep the hedge?
Your initial hedge is long stock.
Now the call position is Less like stock[1], so your short call is now less short, so you should drive towards more short — sell IBM when it sinks.

[1] Visualize the curved hockey stick of a Long call. You move towards the blade.

Hockey stick is one of the most fundamental things to Bear in mind.

IRS intuitively – an orange a day#tricky intuition

Selling an IRS is like signing a 2-year contract to supply oranges monthly (eg: to a nursing home) at a fixed price.

Subsequently orange price rises, then nursing home is happy since they locked in a low price. Orange supplier regrets i.e. suffers a paper loss.

P241 [[complete guide]] — Orange County sold IRS (the oranges) when the floating rate (orange price) was low. Subsequently, in 1994 Fed increased the target overnight FF rate, which sent shock waves through the yield curve. This directly lead to higher swap rates (presumably “par swap rates”). Equivalently, the increased swap rate indicates a market expectation of higher fwd rates. We know each floating rate number on each upcoming reset date is evaluated as a FRA rate i.e. a fwd-starting loan rate.

The higher swap rate means Orange County had previously sold the floating stream (i.e. the oranges) too cheaply. They lost badly and went bankrupt.

It’s crucial to know the key parameters of the context, otherwise you hit paradoxes and incorrect intuitions such as:

Coming back to the fruit illustration. Some beginners may feel that rising fruit price is good for the supplier, but wrong. Our supplier already signed a 2Y contract, so the rising price doesn’t help.

hazard rate – online resources

is decent —

Average failure rate is the fraction of the number of units that fail during an interval, divided by the number of units alive at the beginning of the interval. In the limit of smaller time intervals, the average failure rate measures the rate of failure in the next instant for those units surviving to time t, known as instantaneous failure rate.

is more mathematical.

http://www.omdec.com/articles/reliability/TimeToFailure.html has short list of jargon

ccy swap^ IRS^ outright FX fwd

currency swap vs IRS
– Similar – exchange interest payments
– diff — Ccy swap requires a final exchange of principal. FX rate is set up front on deal date

currency swap vs outright fx fwd?
– diff — outright involves no interest payments
– similar — the far-date principal exchange has an FX rate. Rate is set on deal date
– diff — the negotiated rate is the spot rate on deal date for ccy swap, but in the outright deal, it is the fwd rate.

currency swap vs FX swap? Less comparable. Quite a confusing comparison.
– FX swap is more common more popular

hazard rate – my first lesson

Imagine credit default is caused only by a natural disaster (say hurricane or tsunami). For a brief duration ΔT (measured in Years), we assume the chance of disaster hitting is λ*ΔT, with a constant [1] λ .

Pr(no hit during    A N Y   5-year period)
= Pr (surviving 5 years)
= Pr (no default for the next 5 years from now)
= Pr (T > 5) = exp(-5λ) , denoted V(5) on P522 [[Hull]]

, where T :=  # of years from now to next hit.

This is an exponential distribution. This λ is called the hazard rate, to be estimated from market data. Therefore it has a term structure, just like the term structure of vol.

More generally,  λ could be assumed a function of t, i.e. time-varying variable, but a slow-moving variable, just like the instantaneous vol. In a noisegen, λ  and vol function as configurable parameters.

In http://www.financial-risk-manager.com/risks/credit/edf.html, λ is denoted “h”, which is assumed constant over each 12-month interval.

“Hazard rate” is the standard terminology, and also known as “default intensity” or “failure rate”.

I feel hazard rate is perhaps the #1 or among top 3 applications of
conditional probability,
conditional distribution,
conditional expectation

So the big effort in studying the conditional probability is largely to help understand credit risk.

bonds ^ swaps – 2 subdomains in FI

3rd and 4th domains would be credit (including muni) and mortgage, but let’s put them aside, despite their very large market sizes.

There’s huge demand for IR swaps and riskfree bonds. To keep things simple (perhaps over-simplifying), we can say
– bonds are income-generation Investments, needed by every investor esp. serious investors including banks, fund managers and pension/insurance.
– swaps (on the long end of YC) and IR futures (on the short end) are needed for risk management (hedging) by large enterprises with interest rate exposures.
Both domains rely on their respective yield curves. The so-called curve instruments are never mixed. Let’s illustrate using USD
– swap curve is built from Libor instruments like Libor swaps, Libor FRA and ED deposits, but not Treasury instruments. In AUD market, there’s no Libor so people use BBSW.
– Treasury curve is built from T and T-futures, not Libor instruments

In Lida’s words, these would be the risky curve (AA curve) vs the riskfree curve (government curve).

Q: how about the OIS curve? I think it’s based on OIS instruments

OIS^Libor — 2 indices

contract maturity –up to 50Y, for both OIS and Libor swaps.

payment frequency – 1Y for long-term OIS swaps. Example – 50 payments for a 50Y OIS swap. If term (ie maturity) is below 1Y, then there’s just one payment, at maturity. See http://www.frbsf.org/economic-research/events/2013/january/federal-reserve-day-ahead-financial-markets-institutions/files/Session_1_Paper_1_Filipovic_Trolle_interbank.pdf

fixing frequency – 1D for OIS. In contrast, for USD Libor swap, typically 3M.

accrual period — Assuming a 3M payment frequency on the floating leg. The underlying “assumption” is a 3M (unsecured) loan to an AA-rated bank. In contrast, the OIS underlying loan is a 1D (unsecured) loan, typically to a bank. The underlying loan tenor is what I call the “accrual period”. Taking USD as example, the standard “accrual period” is 3M. So if you want a swap with floating accrual period of 6M, then you need to do a tenor basis swap. I feel OIS is simple. The accrual period is always 1D, as the underlying loan is 1D. The 1Y payment frequency is less important.

Both are unsecured loans, but OIS is a closer proxy for the riskfree rate. I guess overnight borrowing by gov (of the named currency) would be a better riskfree rate, but no such thing.

Libor IRS has zero value at inception. The trade execution price is the fixed rate, which equals the “average” of the expected floating payments… Overnight Index swap is a similar contract. The average is geometric, and the reference (i.e. floating) rate is the FF/EONIA/SONIA/…

https://quant.stackexchange.com/questions/29644/difference-between-ois-rate-and-fed-funds-rate has concise details.

fx swap – mostly used for funding

Soundbyte — FX swap is a popular alternative to (secured) bank loan.

www.rba.gov.au/publications/bulletin/2010/jun/pdf/bu-0610-7.pdf is the best article to shed light on the “funding” usage of FX swap. (By the way, It also covers the ccy swap i.e. xccy IRS, which tends to be confused with fx swap.)

The term “funding” is unnatural to me. “Funding” basically means borrowing money for a fixed repayment period. Say I have a big project and need $555m. I typically borrow from a bank or issue a bond. Note with each “funding” requirement, there's a pre-defined repayment timeframe.

A similar verb is “raising” fund.

implicits in an ED fut price

At the heart of this price thingy is a __fwd-starting loan__. The price is related to the interest rate on this loan, also known as FRA rate or simply fwd rate. Traders basically guess at (“bet and “trade” are less intuitive) this rate.

Implicit – loan is 3M tenor

Implicit – loan starts 2 days after expiry of the futures contract.

Implicit – this fwd interest rate is always, always, always annualized

bond yield – liquidity premium ^ credit spread

I guess an issuer A’s bond may trade at a Higher yield than an issuer B’s bond, even if A’s credit quality is higher. Paradox?

One reason i can imagine is liquidity preference. Suppose you are an investor. Suppose the 2 bonds have the same coupon and other features. You as well as the market know that bond A is (slightly) less likely to default than B, but you may still be willing to pay a bit more for B, because it’s easier to sell it when you need cash.

Bond A may be an unknown entity, traded on very few markets (including bank’s private distribution networks), so there are far fewer bids of A then B. The lower market access leads to lower buyer competition, lower bid prices when you are forced to sell. 
Therefore, a prudent investor may be willing to pay more for bond B.
Since many investors behave similarly, B gets higher buyer competition, higher valuation and lower yield (spread).

Similarly, McDonald burgers may be smaller but more expensive than the no-name burger next door — liquidity

fwd curve^spot curve: different x-axis

ICAP terminology —
effDate :=  accrual starts. Therefore, fwd-starting contracts have effDate long after execution date.
maturity:= accrual ends.
tenor := accrual period length := maturity – effDate

A Fwd curve consisting of 22 points describes 22 FRA deals with identical accrual length, but 22 different accrual-start dates. (Both Mark Hendricks and NYU agree.)

spot rate r(t)= rate of a loan starting today, with maturity = t
fwd rate f(t) = rate of a FRA starting at t, with a standard and Implicit tenor (say, 6M)

  • spot curve with 33 numbers describes loans with 33 different loan maturities
    • discount curve is similar
  • fwd curve with 22 numbers describe FRA deals with Identical accrual length, but 22 different fwd-start dates.

So the x-axis has different meanings! Relationship between the 2 curves are described by Mark Hendricks + Bruce Tuckman with an intuitive explanation!

I believe the fwd curve (with /infinitesimal/ tenor) is based on the theoretical concept of instantaneous fwd rate (IFR)… but let’s not get bogged down with technicalities.

fwd px ^ px@off-market eq-fwd

fwd price ^ price of an existing eq-fwd position. Simple rule to remember —
QQ) not $0 — fwd price is well above $0. Usually close to the current price of the asset.
EE) nearly $0 — current “MTM value” (i.e. PnL) of an existing fwd contract is usually close to +-$0. In fact, at creation the contract has $0 value. This well-known statement assumes both parties negotiated the price based on arb pricing.

Q: With IBM fwd/futures contracts, is there something 2D like the IBM vol surface?

2 contexts, confusing to me (but not to everyone else since no one points them out) —

EE) After a fwd is sold, the contract has a delivery price “K” and also a fluctuating PnL/mark-to-market valuation “f” [1]. Like a stock position (how about a IRS?) the PnL can be positive/negative. At end of day 31/10/2015, the trading venue won’t report on the MTM prices of an “existing” contract (too many), but the 2 counter-parties would, for daily PnL report and VaR.

If I’m a large dealer, I may be long/short a lot of IBM forward contracts with various strikes and tenors — yes a 2D matrix…

[1] notation from P 109 [[hull]], also denoted F_t.

QQ) When a dealer quotes a price on an IBM forward contract for a given maturity, there’s a single price – the proposed delivery price. Trading venues publish these live quotes. Immediately after the proposed price is executed, the MTM value = $0, always

The “single” price quoted is in stark contrast to option market, where a dealer quotes on a 2D matrix of IBM options. Therefore the 2D matrix is more intrinsic (and well-documented) in option pricing than in fwd contract pricing.

In most contexts in my blog, “fwd price” refers to the QQ case. However, in PCP the fwd contract is the EE type, i.e. an existing fwd contract.

In the QQ context, the mid-quote is the fwd price.

Mathematically the QQ case fwd price is a function of spot price, interest rate and tenor. There’s a simple formula.

There’s also a simple formula defining the MTM valuation in EE context. Its formula is related to the QQ fwd quote formula.

Both pricing formulas derived from arbitrage/replication analysis.

EE is about existing fwd contracts. QQ is about current live quotes.

At valuation time (typically today), we can observe on the live market a ” fwd price”. Both prices evolve with time, and both follow underlier’s price S_t. Therefore, both prices are bivariate functions of (t,S). In fact, we can write down both functions —

QQ: F_t = S_t / Z_t ….. (“Logistics”) where Z_t is the discount factor i.e. the T-maturity discount bond’s price observed@ t
EE: p@f = S_t – K*Z_t

( Here I use p@f to mean price of a fwd contract. In literature, people use F to denote either of them!)

To get an intuitive feel for the formulas, we must become very familiar with fwd contract, since fwd price is defined based on it.

Fwd price is a number, like 102% of current underlier price. There exists only one fair fwd price. Even under other numeraires or other probability measures, we will never derive a different number.

In a quiz, Z0 or S0 may not be given to you, but in reality, these are the current, observed market prices. Even with these values unknown, F_t = S_t / Z_t formula still holds.

Black’s model – uses fwd price as underlie, or as a proxy of the real underlier (futures price)

Vanilla call’s hockey stick diagram has a fwd contract’s payoff curve as an asymptote. But this “fwd contract’s payoff curve” is not the same thing as current p@f, which is a single number.

hockey stick – asymptote

(See also post on fwd price ^ PnL/MTM of a fwd position.)

Assume K = 100. As we get very very close to maturity, the “now-if” graph descends very very close to the linear hockey stick, i.e. the “range of (terminal) possibilities” graph.

10 years before maturity, the “range of (terminal) possibilities” graph is still the same hockey stick turning at 100, but the now-if graph is quite a bit higher than the hockey stick. The real asymptote at this time is the (off-market) fwd contract’s now-if graph. This is a straight line crossing X-axis at K * exp(-rT). See http://bigblog.tanbin.com/2013/11/fwd-contract-price-key-points.html

In other words, at time 0, call value >= S – K*exp(-rT)

As maturity nears, not only the now-if smooth curve but also the asymptote both descend to the kinked “terminal” hockey stick.

investment bank as IRS mkt-maker

See also – Trac Consultancy course handout includes many practical applications of IRS.

A) A lot of (non-financial) corporations (eg. AQQ) have floating interest cost from short term bank _loans_. (I did the same with Citibank SG. Every time I rolls the loan, the interest is based on some floating index.) For risk control and long term planning, they prefer a fixed borrowing cost. They would seek IRS dealers who gives a quote in terms of the swap rate — dealer to charged fixed interest and “Sell floating interest” i.e. “Sell the swap” or “Sell Libor”.

A muni IRS dealer would determine her swap rate using 70% Libor as the floating rate. For each tenor (3 months to 2 years) the ratio is slightly different from 70%.

B) On the other side of the river, a lot of bond issuers (eg IBM) have a fixed interest cost, but to lower it they want floating cost (pay floating). So they find IRS dealers who quote them a swap rate — dealer to PAY fixed and Buy floating interest Income, i.e. dealer Buy the swap.

It's important to get the above 2 scenarios right.


Q: Is it possible for Company A to directly trade with Company B without a dealer? It's improbable to find such a trading partner at the right time. Even if there is, transaction cost is probably too high.

The same dealer could give quotes to both clients. The 2 swap rates quoted are like the bid/ask “published” by the dealer. Dealer might want to pay 500bps for Libor; and simultaneously want to charge (receive) 530bps for Libor.

Dealer doesn't really publish the 2 swap rates because each IRS contract is bespoke. If a dealer happens to have both client A and B then dealer is lucky. He can earn the difference between the 2 swap rates. Usually there's not a perfect match on tenor and amount etc. In such a (normal) case, dealer has outstanding exposure to be hedged. They hedge by buying (selling also?) Eurodollar futures or trading gov bonds with repo.

In summary

AQQ's Motivation to pay fixed – predictable cost

IBM's Motivation to pay floating – lower cost

IRS motivations – a few tips

See also – Trac Consultancy course handout includes many practical applications of IRS.
see also — There’s a better summary and scenarios in the blog on IRS dealers

I feel IR swap is flexible and “joker card” in a suite — with transformation power.

Company B (Borrower aka Issuer) wants to borrow. Traditional solution is a bond issue or unfortunately …. a bank loan (most expensive of all), either fixed or floating rate. A relatively new Alternative is an IRS.

Note bank loan is the most expensive alternative (in terms of capital charge, balance sheet impact …), so if possible you avoid it. Mostly small companies with no choice take bank loans.

Motivation 1  relative funding advantage
Motivation 2 for company B – reduce cost of borrowing fixed
Motivation 3 for Company B – betting on Libor.
* If B bets on Libor to _rise, B would “buy” the Libor income stream of {12 semi-annual payments}, at a fixed (par) swap rate (like 3.5%) agreed now, which is seen as a dirt cheap price. Next month, the par swap rate may rise (to 3.52%) for the same income stream, so B is lucky to have bought it at 3.5%.
* If B bets on Libor to _drop, B would “sell” (paying) the Libor income stream

Motivation 4 to cater to different borrowing preferences. Say Company C is paying a fixed 5% interest, but believes Libor will fall. C wants to pay floating. C can swap with company A so as to pay libor. C will end up paying floating interest to A and receive 5.2% from A to offset the original 5% cost.

Why would A want to do this? I guess A could be a bank.

eq-forward – basic questions to internalize

See also post on equity forward. Better become very very comfortable answering these questions. They should be in your blood:)

Q: daily mark to market of an existing position, on some intermediate date “t” before maturity.

Q: market risk of an existing long position?
A: similar to a simple long spot position. When underlier appreciates, we have a positive  PnL. “Logistics”.

Q: delta of  such an existing fwd contract?

There are many relationships  among many variables –

K, T — part of the contract specification
Z0, S0, — observable today
F0 — defined in the EE context as the MTM value of a new position. Almost always $0
ZT := 1.0, STFT := ST – K
Zt, St, Ft,  — where t is an intermediate time between now and T. Since t is in the future, these values are unknown as of today.

An interviewer could ask you about the relationship among any 3 variables, or the relationship among any 4 variables.

Warning — I use F0 to denote today’s price of an off-mkt fwd contract with K and T. Some people use F0 to denote the fwd price of the stock S.

FX swap ^ FX loans – popularity=off balance sheet

One of the best-known motivation/attraction of FX swap over traditional FX loans is – off balance sheet.

The Trac consultancy trainers gave many specific examples. Context is commercial banking, because unlike listed securities, a “buy-side” has no way to trade FX swap on some exchange without a big bank facilitating. Most FX inventories are held by banks (even more than governments apparently). The biggest players are invariably the international banks + central banks, not big hedge funds.

Specifically, the context is a client (like IBM) coming to a commercial bank for a FX solution. Commercial banks are heavily regulated, more so than investment banks. One of the regulations is capital adequacy. Traditional loans to IBM would tie up too much capital in the bank – capital inefficiency. Even for the client (IBM), I feel borrowing would often require collateral.

FX swap in contrast requires much less capital.

A different form of IRS off-balance-sheet benefit is given in http://bigblog.tanbin.com/2014/05/irs-off-balancesheet-briefly.html, applicable for a buy-side as well.

ccy risk in FX swap ^ forward outright

In short, FX swap entails no currency risk because no future FX rate enters the PnL formula. Currency risk, or FX risk, refers to the uncertainty/hazard of exchange rate movement during a “holding period”, when we have an “exposure”.

For a longer explanation, let’s start with a simple spot FX transaction. As soon as we convert to or from our account currency (HKD for example), we have an open (long or short) position in some silver – I treat any other currency as a commodity. Price movement in silver causes paper gain or loss. If the notional is large, then I lose sleep, until I close the position and have everything in my home currency again.

In terms of FX risk, a forward outright is different from a spot trade only logistically. As soon as we agree on a price and execute, I take on an open position and open exposure, way before the settlement date.

(In terms of credit risk however, the outright differs substantially from the spot trade.)

The simplest no-position scenario is the fixed-fixed cross-currency swap. On near date, we exchange principals – say HKD 7m vs USD 1m. On far date, we return each other the exact same amounts, not a single cent different. In between, all the pre-agreed interest payments are exchanged too, where one interest rate can be many times higher than the other. No FX risk on the principal amount.

Finally we come to the more important instrument – FX swap. It doesn’t create any open position. On trade date counterparties agree on the two exchange rates, leaving no uncertainty or exposure to the market.

use swap point bid/ask to derive FX fwd outright bid/ask

(label – FX)

See other posts on fwd swap point interpretation.

See other posts on how to compute fwd outright bid/ask without swap points — using interest rate bid/ask.

Given spot bid/ask is 105.30/105.35 (whatever ccy pair – unimportant). Suppose swap points are quoted 1.10/1.05, we can deduce the asset currency is trading at a fwd Discount[1], because the swap quote is “high/low”. Fwd Discount means that fwd outright price is Lower than spot price. Always treat the first currency as a commodity like silver.

Fwd outright bid/ask of the “silver” are 105.30 – 1.10 / 105.35 – 1.05

Note this is not some expectation/prognosis of an upcoming event, to-be-known. Instead, the 105.30 – 1.10 = 104.20 price is for execution today. Only the settlement is 1Y later.

[1] Even if we don't know “Discount”, we can still figure out whether to subtract or add the swap points. Golden Rule [2] is, fwd outright bid/ask spread must be wider than spot bid/ask spread.

Therefore, Since swap bid (1.10) is Bigger than ask, we must Subtract it from spot bid. Subtracting a bigger number from bid is the only way to WIDEN the spread.

[2] in fact, the final bid/ask spread in fwd outright pips equals the spot spread + |swap point spread|. Here we take the abs value because we don't care if the swap points are quoted “high/low” or “low/high”.

FX Vol – Butterfly or Strangle@@

[[Managing Currency Risk Using Foreign Exchange Options]] says

Butterfly is a combination of ATM straddle and an OTM strangle, and is a more exact way of trading the smile of volatility.

The OTM strangle relates net premium, in volatility terms, over the ATM ( volatility) rate. The purchase (or sale) of an OTM Strangle still leaves the trader open to a change in the ATM rates, so it’s possible for a change in the smile shape to be compensated by a change in the ATM rates. To be more exact, trader can lock in the difference between the two (ATM vs OTM volatilities) by trading the butterfly spread.

what departments use the yield curve

In one mkt risk system, the USD (no other currencies!) yc is used to compute FX swap points. That’s the only usage of the yc in that system.

Why some large investment banks have a sizable IT team supporting the yield curve(s) and update it a few times a day? I was told

… that a big user is the IRS desk. IRS contracts last many years. A portfolio may be highly sensitive to the interest rate at some point on the yc. A small shift of the yc may tip the entire portfolio from ITM to OTM. Note ITM/OTM is always for the swap dealer.

I feel if a portfolio is sensitive to the yc, then the trader needs up-to-the-hour yc to help guide his quoting and trading decisions.

dark pools – a few observations

Most common Alt Trading Service is the dark pool, often operated by a sell-side bank (GS, Normura etc).

A “transparent” exchange (my own lingo) provides the important task of _price_discovery_. A dark pool doesn’t. It receives the price from the exchanges and executes trades at the mid-quote.

Market order can’t specify a price. You can think of a market buy order as a marketable limit order with price = infinity. Therefore, when a market order hits a limit order, they execute at the limit price. When 2 limit orders cross, they execute at the “earlier” limit price.

Therefore, on the exchange, I believe all trades execute either on the best bid price or best ask. I guess all the mid-quote executions happen on the ATS’s.

Dark pool is required to report trades to the regulator, but often with a few sec longer delay than an exchange.

Dark pool may define special order types beside the standard types like limit orders or market orders.

Forex is quote driven, not order driven. Forex has no exchange. The dominant market is the interbank market. Only limit orders [1] are used. However, within a private market operated by a single dealer, a “market order” type can be defined. I feel the rules are defined by the operator, rather than some exchange regulator.

[1] A Forex limit order is kind of fake – unlike the exchange’s guarantee, when you hit a fake limit order that dealer may withdraw it! I believe this is frowned upon by the market operator (often a club of FX banks), so dealers are pressured to avoid this practice. But I guess a dealer may need this “protection” in a fast market.

use YC slope to predict 5Y bond’s return over the next 12M

Mark’s lecture 4 describes a famous “YC” carry trade strategy using T bonds. To keep things simple, we use zero bonds (coupon bonds same). Given a bond of 5Y maturity, next year’s return is defined as the NAV 12M from now vs the current NAV. In other words, the ratio of next year’s price over today’s price. It’s probably slightly above 1.0 or perhaps below 1.0.

This return factor is observable 365 days later, but we can predict it using the currently observable term spread, i.e. the 5Y yield – the 3M yield seen today. 
Idea is, if the slope is steep, then we expect that return to be high. Steep slope basically means we observe high yield at the 5Y point on today’s yield curve. Suppose it’s a high 8.8%. If we were to hold the 5Y bond to maturity, we would realize approx. (without compounding) 44% return. Instead, we actually plan to sell the bond next year, so we are forecasting this bond price next year, effectively the 4Y point on next year’s yield curve. (Apply P/Y conversion)
We expect that yield to remain around 8.8%, or equivalently, we expect the market yield on this same bond to remain. That would be higher than the riskfree rate (represented by the 1Y yield, say 0.8%).

However, If we are unlucky, the return factor (observable in a year) could come below the riskfree return factor today. (Note both deals cover the same loan period.)
* But then, we could cancel our plan and hold the bond to maturity and realize a total return of 44%. This is somewhat risky, because bond yield could rise further beyond 8.8%, hurting our NAV before maturity.
* Crucially, if the return over the next 12 months turns out to be lower than riskfree rate, then the subsequent 4 years must return more than 8.8% pa, since the return-till-maturity is fixed at 44%.

I have a spreadsheet illustrating that yield shifts in the next year may hurt the then NAV but the total return till maturity is unaffected.

EH (expectation hypothesis) actually says there’s no reason to prefer the 5Y vs the riskfree rate. Contrary to EH, empirical data show that today’s slope is a good predictor of the return over the next 12 months.

increasing corporate bond issues -> swap spread narrowing

Look at the LTCM case.

Almost all the issuers are paying fixed coupons. Many of them want to swap to Receive fixed (and pay floating). This creates an (increasing supply for the LFS i.e. Libor floating stream and) increasing demand on the fixed rate. Suppose Mark is the only swap dealer out there, so he could lower the swap spread to be as Low as he likes, so low that Mark’s paying fixed rate is barely above the treasury yield.

Note increasing demand on the fixed rate doesn’t raise it higher but rather hammer it down. Here’s why — if more job seekers now want to earn a fixed salary as a carpenter, then that fixed salary would Drop.

Oversupply to bonds would suppress bond prices, and increase bond yields. Oversupply of bank loans suppresses interest rate. I get many credit line promotion calls offering very low interest rates.

Now I feel it’s easier to treat the Libor floating stream (LFS) as an asset. The price is the swap spread.

When there’s over-supply of LFS, swap spread will tighten;
When there’s over-demand of LFS, swap spread will widen.

IRS – off-balancesheet #T-bond repo

The LTCM case P12 illustrated (with an example) a key motivation/benefit of IRS — off balance sheet. The example is related to the swap spread trade briefly described in other posts.

For a simple T-bond purchase with repo financing, the full values (say $500m) of the bond and the loan appear on the balance sheet, increasing the fund’s leverage ratio. In contrast, if there’s no T-bond purchase, and instead we enter an IRS providing the same(?? [1]) interest rate exposure, then the notional $500m won’t appear on balance sheet, resulting in a much lower leverage ratio. Only the net market value of the existing IRS position is included, usually a small value above or below $0. (Note IRS market value is $0 at inception.)

[1] An IRS position receiving fixed (paying float) is considered similar to the repo scenario. The (overnight?) rollling repo rate is kind of floating i.e. determined at each rollover.

Other positions to be recorded off balance sheet ? I only know futures, FX swaps, …

UIP carry trade n risk premium

India INR interest could be 8.8% while USD earns 1.1% a year. Economically, from an asset pricing perspective, to earn the IR differential (carry trade), you have to assume FX risk, specifically the possible devaluation of INR and INR inflation during the hold period. 

In reality, I think INR doesn't devalue by 7.7% as predicted by UIC, but inflation is indeed higher in India.
In a lagged OLS regression, today's IR differential is a reasonable leading indicator or predictor of next year's exchange rate. Once we have the alpha and beta from that OLS, we can also write down the expected return (of the carry trade) in terms of today's IR differential. Such a formula provides a predicted excess return, which means the carry trade earns a so-called “risk premium”. 
Note, similar to the DP, this expected return is a dynamic risk premium (lead/lag) whereas CAPM (+FamaFrench?) assumes a constant time-invariant expected excess return.. 

alpha or beta@@ illustrated with treasury spread

Mark's slide P7.47 on Liquidity risk posed the question — the widening spread between on-the-run vs off-the-run treasuries invite an arbitrage strategy. The excess return is often considered alpha. Maybe it is actually beta, because this excess return is not free lunch. Instead it is a reward for taking on liquidity risk. Off the run is less liquid when you are forced to sell it before maturity. It's also less valuable as a collateral.

Bottom line – Any excess return that's associated with some risk is beta not alpha.

collateralized 100% financing on a treasury trade

Develop instincts with these concepts and numbers — common knowledge on IR trading desks. P10 of the LTCM case has an example on Treasury trading with repo financing.

Most buy-side shops work hard to get 100% collateralized financing. Goal = avoid locking up own capital. 100% means buying $100m T bond and immediately pledge it for repo and use the borrowed $100m for the bond purchase. If only $99m cash borrowed (1% haircut), then LTCM must commit $1m of own capital, a.k.a. $1m “equity investment”.

P14 explains that many buyers choose overnight and short term repo, but LTCM chose 6-12M term repo, where the repo rate is likely higher.

LTCM managed to keep most of the $6.7b capital in liquid cash, generating about 5% interest income annually. This $350m interest adds almost 50% on top of the average $750m trading profit annually.

4th data source to a yield curve – year-end Turn

See http://www.jonathankinlay.com/Articles/Yield%20Curve%20Construction%20Models.pdf
for more details.

The year-end turn of the yield curve is defined as the sudden jump in yields during the change of the year. This usually happens at the end of the calendar year, reflecting increased market activity related to
year-end portfolio adjustments and hedging activity….When there is a year turn(s), two discount curves are
constructed: one for turn discount factors and one for the discount factors calculated from the input instruments after adjustments and the discount factor at any time is the multiplication of two.

trading swap spread – LTCM case (with wrong intuitions

See Harvard Biz School case study 9-200-007 on LTCM. I feel this is a good simple scenario to develop analytic instinct/intuition about IRS.

I believe USD swap spread is similar to the TED (which is 3M). A very narrow TED means on the lower side T (i.e. treasury) yield too high and on the upper side fwd Libor too low.

T yield too high means T bonds too cheap. Therefore, LTCM would BUY T bonds.

Expected series of Libor cashflow is too low, so the equivalent fixed leg is also too low. Therefore LTCM would PAY the fixed rate. The par swap rate is the price you lock in today, which buys you the Libor stream, which you believe to be rising.

In the orange case, you as a Libor/orange buyer lock in a price today and you expect the oranges to get bigger soon.

For a 10Y swap, we are saying the forward Libor rates over 3->6M, 6->9M, … 120->123M… are too low and may rise tomorrow. There are many wrong ways to interpret this view.

correct – Since the floating income will rise, we would want to receive those future Libor interests.


correct – We can think of the floating leg as a hen giving eggs periodically. The market now forecasts small eggs, but LTCM feels those eggs will be bigger, and the hen is under valued. So LTCM buys the hen by paying the (low) fixed rate.

trading swap spread – LTCM case, again

Here’s a simpler way to look at it. When the swap spread is too narrow, T yield is too high and swap fixed rate is too low. …. (1)

Key – use a par bond as a simple (but not simplistic) example, so its yield equals its coupon interest rate.

Now we can rephrase (1) as — T bond interest too high and swap fixed rate too low, and they are going to widen. Now it’s obvious we should Buy to receive T interest (too high). And we pay the swap fixed rate (too low), and consequently receive Libor.

When we say “swap rate is too low and is likely to rise in 4 months”, i think we are predicting a “rise” in Libor. Swap rate is like a barometer of the Libor market and the Libor yield curve.

A simple “rise” is a parallel shift of the Libor yield curve. A less trivial “rise” would involve a tilt. Rise doesn’t mean upward sloping though.

It’s rather useful to develop instinct and intuition like this.

difference – discount factor ^ (Libor,fwd,spot…)rates

Discount factor is close to 1.0, but all the rates are annualized and usually between 0.1% ~ 8%.

This simple fact is often lost in the abstract math notations. When I get a long formula with lots of discount factors, forward rates, (forward) Libor rates, floating payments, future fixed payments… I often substitute typical numbers into the formula.

Also, due to annualizing, the rate number for overnight vs long tenors (like 1Y) are similiar, at least the same order of magnitude.

FX vs IR trading desks, briefly

Now I know that in a large sell-side, FX trading is “owned” by 2 desks – the “cash” FX desk and the IR desk. Typically, anything beyond 3 months is owned by the Interest Rate desk (eg STIRT). It seems that these FX instruments have more in common with interest rate products and less in common with FX spot. They are sensitive to interest rates of the 2 currencies.

In one extreme case every fx forward (outright?) deal is executed as a FX spot trade + a FX swap contract. The FX swap is managed by the interest rate desk.

FX vol is a 3rd category, a totally different category.

y use OIS instead of Libor discounting — random notes

Cash-flow discounting (to Present Value) should use a short rate, “instantaneously short”, ideally a risk-free rate, which is theoretical. In reality, there are various candidates —

Candidate: treasury bill rate. The rate is artificially low due to tax benefit leading to over-demand, higher price and lower yield. There are other reasons explained in ….

Candidate: Libor. In recent years, Libor rates are less stable compared to OIS. Libor is also subject to manipulation — the scandals. OIS is actual transaction rate, harder to manipulate.

Q: why OIS wasn’t chosen in the past?
%%A: not as actively traded (and influential) as Libor

valuation of existing IR swap – example

Based on http://www.xavier.edu/williams/centers/trading-center/documents/research/edu_ppts/03_InterestRateSwaps.ppt (downloaded to C:\0x\88_xz_ref)

On P54 the “closing a swap position” discussion is … very relevant. Start at the example on P57.

On T+0, enter 5.5%/Libor swap as fixed payer.

On T+1Y, prevailing (par) swap rate drops to 5%. Bad for the fixed payer as she has commitment to pay 5.5%. She wants out, and she doesn’t need any more loan. You can assume she has cancelled her project altogether. So she would hedge out her floating exposure and realize any loss on the fixed leg.

Specifically, she enters a new swap as a fixed Receiver this time, receiving (the lower) 5%. The new floating leg perfectly cancels the existing floating leg, with identical payment dates.

As a result, for the next 4 semi-annual payments, she would receive 2.5% and pay 2.75% every time. This is the kind of loss she must accept when closing the swap in an unfavorable market. If you sum up the present value of these 4 negative cashflows, you see the (negative) present MV of the fixed position. (Note each swap deal has a $0 market value at inception.)

(The “fixed position” means the position of the fixed Payer.)

As of  T+1Y, the fixed position has a negative mark-to-market value given on P60, -$94,049 on a $10m notional.

It follows that to the original fixed Receiver, this existing swap deal now has a positive market value. Intuitively, this receiver is paying a below-market rate (5%/year) to receive the stream of floating coupons (i.e. the silver). The same stream is currently selling at 5.5%.

Yes it’s confusing! I feel the keys are
1) how to cancel out the floating leg exposure. You will then figure out that to close the swap, you need to take up a new fixed leg.
2) That would tell you the upcoming cashflows are positive or negative.
3) By summing up the PV of those cash flows you get the current MV.

Final MV formula is on P70.

selling an existing IR swap@@

I guess technically we can’t sell an IRS as it’s not a product like an orange (or a house, or an option) with an owner. A IRS is a long-term bilateral agreement. Analog? I can’t “sell” my insurance policy to someone else.

A liquid swap market lets us offset our Libor exposure —

Suppose I’m a Payer in Deal 1 with Citi, to receive Libor and pay fixed 4.5%. Five hours (or 5 days or 5 months) later, I could become a Receiver in a JPM deal (Deal 2) to pay Libor and receive fixed 4.6%. Therefore I get rid of my Libor exposure, as long as the reset dates are identical between Deal 1 and Deal 2. But strictly speaking I haven’t Sold an existing swap. Both are long-term commitments that could in theory be unwound (painful) but never “sold” IMO.

By market convention, the counterparty paying the fixed rate is called the “payer” (while receiving the floating rate), and the counterparty receiving the fixed rate is called the “receiver” (while paying the floating rate).

PCP with dividend – intuitively

See also posts on PCP.
See also post on replicating fwd contract.

I feel PCP is the most intuitive, fundamental and useful “rule of thumb” in option pricing. Dividend makes things a tiny bit less straightforward.

C, P := call and put prices today
F := forward contract price today, on the same strike. Note this is NOT the fwd price of the stock.

We assume bid/ask spread is 0.

    C = P + F

The above formula isn’t affected by dividend — see the very first question of our final exam. It depends only on replication and arbitrage. Replication is based on portfolio of traded securities. (Temperature – non-tradable.) But a dividend-paying stock is technically non-tradable!

* One strategy – replicate with European call, European put and fwd contract. All tradable.

* One strategy – replicate with European call, European put, bond and dividend-paying stock, but no fwd contract. Using reinvestment and adjusting the initial number of shares, replication can still work. No need to worry about the notion that the stock is “non-tradable”.

Hockey stick, i.e. range-of-possibility graphs of expiration scenarios? Not very simple.

What if I must express F in terms of S and K*exp(-rT)? (where S := stock price any time before maturity.)

  F = S – D – K*exp(-rT) … where D := present value of the dividend stream.

predicted future px USUALLY exceeds current px – again

This is a pretty important concept …

Extreme example – Suppose home price is believed to be unpredictable or unstable for the next 3 months[1], and short term rental is impossible, and there are many equivalent houses on sale. You just bought one of these equivalent houses but need it in 3 months and you would have all the cash by then. Do you prefer to “settle” (i.e. pay cash and get key) now (A) or (B) in 3 months? You prefer B because A means you must start paying mortgage interest 3-month earlier.

Now suppose seller exploits your preference for B, and asks $1 more to do a fwd deal (B) instead of a spot deal (A), you would be wise to still prefer B because interest amount is likely to be thousands.

So $1 is too cheap. But what’s a fair price for the fwd deal? I think it’s exactly the spot price plus the mtg interest amount. For most securities, fwd price [2] is Higher than spot. (A few assets are exceptions and therefore important[3].) First suppose fwd price == spot price as of today, and ignore the positive/negative signs below —

* if interest_1 < rent_3, then seller gains. Some competing seller would sacrifice a bit of gain to sell at a lower fwd price. Fwd price is then driven down below spot price. This is the high-coupon case.
* if interest_1 > rent_3, then seller loses. She would simply reject the proposed trade. She would have to charge a Higher fwd price to compensate for her loss. This is the usual case, where rent_3 is $0 and there’s no repo or rent market for this asset.

I feel the fair theoretical fwd price is not affected by implied volatility, or by any kind of trend. A trend can continue or reverse. I feel the calculation of fwd price is based on assumption of constant asset price or random movement for the next x months.

[1] I think in most cases of fair pricing we assume the asset’s price has no up/down trend.
[2] If the spot contract doesn’t have a pair of start/end dates, i.e. a straightforward “cash-on-delivery” instrument, then I think in many cases “fwd price” means ” delayed settlement”.

[3] Their fwd price is Lower —
– High-coupon bonds such as treasury
– High-dividend stocks
– many currency pairs

Why the premium vs discount? There’s arbitrage mathematics at play. For most products, a fwd seller could 1) borrow cash to 2) buy the underlier today, 3) lend it out for the fwd term (say 90 days), and 4) deliver it on the fwd start date as promised. All deals are executed simultaneously today, so all prices fixed together, and a profit if any is locked in.

replicate eq-fwd contract, assuming a single dividend

See also

Note replication portfolio is always purchased as a bundle, sometime (time t) before expiry (denoted time T).

First, let’s review how to replicate a forward contract in the absence of dividends. The replication portfolio is {long 1 share, short K discount bonds}. To verify, at T the portfolio payout is exactly like long forward. By arbitrage argument, any time before expiry the portfolio value must at all times equal the fwd contract’s price. I will spare you the math formula, since the real key behind the math is the replication and arbitrage.

Now, suppose there’s a percentage dividend D paid out at time Td before T. In this case, let’s assume the dividend rate D is announced in advance. To reduce the abstractness, let’s assume D=2%, K=$100, the stock is IBM. We are going to reinvest the dividend, not use it to offset the purchase price $100. (This strategy helps us price options on IBM.)

The initial replication portfolio now adjusts to –{ long 0.98 IBM, short 100 discount bonds}. At T, the portfolio is exactly like long 1 forward contract. Please verify!

(In practice, dividends are declared as fixed amount like $0.033 per share whatever the stock price, but presumably an analyst could forecast 2%.)

In simple quant models, there’s a further simplification i.e. continuous dividend yield q (like 2% annually). Therefore reinvesting over a period A (like 1Y), 1 share becomes exp(qA) shares, like exp(0.02*1) = 1.0202 shares.

Q: delta of such a fwd contract’s pre-maturity value? Math is simple given a good grip on fwd contract replication.
A: rep portfolio is { +1 S*exp(-qT),     -K bonds }.
A: key concept — the number of shares (not share price) in the portfolio “multiplies” (like rabbits)  at a continuous compound rate of q. Think of q = 0.02.
A: In other words

   F0 = S0*exp(-qT) – K*Z0

Differentiating wrt S0, delta = exp(-qT), which degenerates to 1 when q=0.

##basic steps in vanilla IRS valuation, again

* First build a yield curve using all available live rates. This “family photo” alone should be enough to evaluate any IRS
* Then write down all (eg 20) reset dates aka fixing date.
* Take first reset date and use the yield curve to infer the forward 3M Libor rate for that date.
* Find the difference between that fwd Libor rate and the contractual fixed rate (negotiated on this IRS contract). Could be +/-
* Compute the net cashflow to occur on that fixing/reset date.
* Discount that cashflow to PV. The discounting curve could be OIS or Libor based.
* Write down that amount.

Repeat for the next reset date, until we have an amount for each reset date. Notice all 20 numbers are inferred from the same “family photo”. Tomorrow under a new family photo, we will recalc/reval all 20 numbers.

Add up the 20 amounts to get the net PV in that position. Since the initial value of the position is $0, this net value is also the PnL.

(instantenous) fwd rate

I believe fwd rate refers to an interest rate from a future start date (like next Aug) to a future maturity date (next Nov). We are talking about the market rate to transpire on that start date. That yet-unknown rate could be inferred (in a risk-neutral sense) today, using the live market rates.

The basic calc is documented in my blog …

When the loan tenor becomes overnight (or, theoretically, shorter than a nanosec), we call it the instantaneous fwd rate. This rate, again, can be estimated. Given observation time is today, we can estimate the fwd rate for different “fwd start dates”, denoted tau. We can plot this fwd rate as a function of tau.

FRA/ED-Fut: discount to fwd settlement date

–Example (from Jeff’s lecture notes)–
Assume on 12 Nov you buy (borrow) a 3×9 FRA struck at 5.5% (paying 5.5%) on 1M notional. On 12 Feb, 6M Libor turns out to be 5.74% , compensation due to you =

$1M x (0.0574-0.055) * 180/360 / (1 + 0.0574*180/360) = $1166.52
——–Notation ——-
Libor fixing date = 12 Feb

“accrual end date” (my terminology) = 12 Aug.

settlement could be either before or (occasionally) after the 6M loan tenor. This example uses (more common) fwd settlement.
disc factor from 12 Aug to 12 Feb = 1/ (1 + 0.0574 * 180/360)
Note the “interest due date” is always end of the 6M accrual period. Since we choose fwd settlement, we discount that cashflow to the fixing date.

annualized interest Rate difference = 5.74 %- 5.5%
pro-rated  interest Rate difference = (0.0574-0.055) * 180/360
difference in interest amount (before discounting) = $1M x (0.0574-0.055) * 180/360. This would be the actual settlement amount if we were to settle after the 6M loan period. Since we choose fwd settlement …

discounting it from 12 Aug to 12 Feb = $1166.52
Now we come to the differences between FRA and ED Futures.
1) a simple difference is the accrual basis. ED futures always assumes 90/360 exactly. FRA is act/360.
2) Another simple difference is, ED Futures always uses 3M libor, so our example must be set on Mars where ED futures are 6M-Libor-based.

3) The bigger difference is the discounting to fwd settlement date or fixing date.
– EDF gets away without the PV discounting. It takes Libor rate as upfront interest rate like in Islamic banking. Since Libor turns out to be 5.74% but you “bought” at 5.5%, the difference in interest amount is, under EDF, due immediately, without discounting to present value.
– the payout, or price, is linear with the Libor rate L.
– this is essentially due to daily mark-to-market margin calculation
* FRA takes Libor rate as a traditional loan rate, where interest is due at end of loan period.
** under late settlement, the amount is settled AFTER the 6M, on the proper “interest due date”. (Linear with L)
** under fwd settlement, the amount is settled BEFORE the 6M, but PV-discounted. This leads to a non-linear relationship with libor rate and convexity adjustment.

fwd disc factor, fwd rate … again

(See other posts in this blog. I think they offer simpler explanations.)

(Once we are clear on fwd disc factor, it’s easy to convert it to fwd rate.)

basic idea — discount an distant future income to tomorrow, rather than to today.

First we need to understand all the jargon around PV discounting which discounts to today…

Fwd discount factor is Discounting an income (or outflow) from a distant future date M (eg Nov) to a “nearer day” T [1] (eg Aug) is based on information available as of today “t” — a snapshot “family photo”. That discount factor could be .98. We write it as P(today, Aug, Nov) = 0.98. The fwd discount function P(t, T, M) can be interpreted as discounting $1 income from Nov (M) to Aug (T), given information available as of today (t). Something like P( Nov -} Aug | today), reversing the order of the 3 dates. As t moves forward, more info becomes available, so we adjust our expectation and estimate to a more realistic value of .80

The core math concept is very simple once you get used to it. $0.7 today grows to $1 in Aug, and $1.25 in Nov. These 2 numbers are implied/derived from today’s prices. These are the risk-neutral expectations of the “growth”. So $1.25 in Nov is worth $0.7 today, i.e.

  P(Nov -} today) = 0.7/1.25. Similarly
  P(Aug -} today) = 0.7/1

These are simple discount factors, Now fwd discounting is

  P( Nov -} Aug | today) = 1/1.25 = 0.8

The original notation is P(today, Aug, Nov) = 0.8.

Note the 0.80 value is not discounted to today, but discounted to next month i.e. Aug only. For PV calculation, we often need to apply discounting on top of the fwd discount factor.

fwd rate is like an interest rate. 0.8 would mean 25% fwd rate.

family photo ^ family video – yield curve

snapshot – The yield curve (yc) is a snapshot.
snapshot – term structure of IR is another name of the yc.
snapshot – discount curve is the same thing

On a given snapshot, we see today’s market prices, yields and rates of various tenors[1]. From this snapshot, we can derive[2] a forward discount factor between any 2 dates. Likewise, we can derive the forward 3M-Libor rate for any target date.

Looking at the formula connecting the various rates, it’s easy to mix the family photo vs the family video.
– family photo is the snapshot
– family video shows the evolution of all major rates (about 10-20) on the family photo.
** an individual video shows the evolution of a particular rate, say the 3M rate. Not a particular bond, since a given bond’s maturity will shrink from 3M to 2M29D in the video.
All the rate relationships are defined on a snapshot, not on a video.

I guess we should never differentiate wrt to “t”, though we do, in a very different context (Black), integrate wrt “t”, the moving variable in the video.

An example of a confusing formula is the forward rate formula. It has “t” all over the place but “t” is really held as a constant. The t in the formula means “on a given family photo dated t”. When studying fixed income (and derivatives) we will encounter many such formula. The photo/video is part of the lingo, so learn it well.

Also, Jeff’s HJM slide P12 shows how the discount bond’s price observed at time t is derived by integrating the inst fwd rates over each day (or each second) on a family photo.

[1] in an idealized, fitted yc, we get a yield for every real-valued tenor between 0 and 30, but in reality, we mostly watch 10 to 20 major tenors.

[2] The derivation is arbitrage free and consistent in a risk-neutral sense.

bond ^ deposit , briefly

Bond and deposit are the 2 basic, basic FI instruments, underlying most interest rate derivatives.

Both pay interest, therefore have accural basis, like act/360 or 30/360

Both have settlement conventions, such as T+2. Note Fed Fund deposit is T+0.

# 1 difference in pricing theories — Maturity value is know for a bond, but in contrast, for some important deposits (money-market deposits) we only know the total market value tomorrow, not beyond. Though many real life fixed-deposits have a long tenor comparable to bonds, the deposits used in pricing theories are “floating” overnight deposits.

# 2 difference — Bond has maturity value exactly $1 and is traded at a discount before maturity, making it an ideal enbodiment of discount factor. A Deposit starts at $1 and grows in value due to interest.

–1) Bonds
eg of bonds — all treasury debts, corp debts, muni debts.

Has secondary market

bonds are the most popular asset for repo.

–2) Deposits is fairly similar to zero bonds.
eg of deposit — Fed Fund deposit, or deposits under other central banks. Unsecured
eg of deposit — Eurodollar deposit, in about 20 major currencies. Unsecured

OIS is based on deposits (Fed Fund deposit)

Libor is based on eurodollar deposits, for a subset (5) of the currencies.

Libor IRS and OIS IRS – all based on deposits.

No secondary market.

I feel deposits tend to be short term (1Y or less)

yield curve -> fwd rate, spot rate …

This is yet another blog post about yield curve, fwd rate, spot rate etc

Let’s say we have a bunch of similar derivative instruments [1] on IBM. Each has an expiry date at each month end. For the Feb instrument, on the expiry date (end of Feb) all uncertainties would vanish and the value of the instrument would be determined/fixed. Therefore it’s practically possible to cash settle on that day. Alternatively the contract may specify a later maturity date (eg 3M from expiry/fixing) for the actual cashflow to occur.

Today, I can record all the current prices of this family of (eg 9) instruments. A minute later I can record their new prices… I keep doing it and get 9 (time-series) streams of live prices.

The “live yield curve” is something similar. The 9 instruments are the 9 deposit maturities we monitor, perhaps {1M, 3M, 6M, 1Y, 2Y, 3Y, 5Y, 10Y, 30Y …} These prices, after converting to yield numbers, actually comprise a 9-point yield curve. From this snapshot yc, we can derive many useful rates, such as (instantaneous) forward rates, spot rates, short rates… all valid at this moment only.

An additional complexity is discounting the cash flow. Whether the cash flow occurs on fixing date or on maturity date, we need to discount to valuation time (moment of observation), using a discounting curve such as the OIS curve.

Every minute, we re-sample live prices, so this 9-point yield curve (and the discount curve) shifts and wiggles by the minute.

[1] Could be bunch of forward contracts, or bunch of binary put options etc

Libor, Eurodollar, OIS, Fed Fund rate … common features

deposit — All are based on the simple instrument of “deposit” — $1 deposited today grows to $1.00x

unsecured — when I deposit my $1 with you, you may go down with my money. Credit risk is low but non-zero.

inter-bank — the deposit (or the lending) is between banks. The lending rate is typically higher when lending to non-banks.

short-term — overnight, 3M etc, up to 12M.

bond investment is safe, in the long run (Hendricks)

If you buy a bond at a $98.5 (1.5% discount from face value), and hold it till maturity, then there’s no uncertainty in how much you will get at the end.

I heard a lot of “common sense” wisdom that bond appreciates and drops with interest rate, and therefore volatile and risky.

(I usually assume default risk is very low for the bonds I consider, at least much lower than the sensitivity to yield.)

However, if indeed a bond loses value due to rate hike, then bond holders always have the “safe” option to hold it till maturity. Its price will eventually rise and end up exactly $100.  Therefore there’s absolutely no uncertainty about the terminal value like there is about options, stocks, or futures contracts.

This is one of the most fundamental features of bond as an asset class. I don’t know another asset having this feature.

eq-fwd contract pricing – internalize

Even if not actively traded, the equity forward contract is fundamental to arbitrage pricing, risk-neutral pricing, and derivative pricing. We need to get very familiar with the math, which is not complicated but many people aren’t proficient.

At every turn on my option pricing learning journey, we encounter our friend the fwd contract. Its many simple properties are not always intuitive. (See P 110 [[Hull]])

* a fwd contract (like a call contract) has a contractual strike and a contractual maturity date.Upon maturity, the contract’s value is frozen and stops “floating”. The PnL gets realized and the 2 counter-parties settle.
* a fwd contract’s terminal value is stipulated (ST – K), positive or negative. This is a function of ST, i.e. terminal value of underlier. There’s even a “range of possibilities” graph, in the same spirit of the call/put’s hockey sticks.
* (like a call contract) an existing fwd contract’s pre-maturity MTM value reacts to 1) passage of time and 2) current underlier price. This is another curve but the horizontal axis is current underlier price not terminal underlier price. I call it a “now-if” graph, not a  “range of possibilities” graph. The curve depicts

    pre-maturity contract price denoted F(St, t) = St                    – K exp(-r (T-t)  ) ……… [1]
    pre-maturity contract price denoted F(St, t) = St exp(-q(T-t)) -K exp(-r(T-t)) .. [1b] continuous div

This formula [1b] is not some theorem but a direct result of the simplest replication. Major Assumption — a constant IR r.

Removing the assumption, we get a more general formula
              F(St, t) = St exp(-q(T-t)) – K Zt
where Zt is today’s price of a $1 notional zero-bond with maturity T.

Now I feel replication is at the heart of everything fwd. You could try but won’t get comfortable with the many essential results [2] unless you internalize the replication.

[2] PCP, fwd price, Black model, BS formula …

Notice [1] is a function of 2 independent variables (cf call).  When (T – now) becomes 0, this formula degenerates to (ST – K). In other words, as we approach maturity, the now-if graph morphs into the “range of possibilities” graph.

The now-if graph is a straight line at 45-degrees, crossing the x-axis at    K*exp(-r  (T-t)  )

Since Ft is a multivariate function of t and St , this thing has delta, theta —

delta = 1.0, just like the stock itself
theta = – r K exp(-r  (T-t)  ) …… negative!

(Assuming exp(-q(T-t)) = 0.98 and
To internalize [1b], recall that a “bundle” of something like 0.98 shares now (at time t) continuously generates dividend converting to additional shares, so the 0.98 shares grows exponentially to 1.0 share at T. So the bundle’s value grows from 0.98St to ST , while the bond holding grows from K*Zt to K. Bundle + bond replicates the fwd contract.

 —————Ft / St is usually (above or below) close to 0 when K is close to S.  For example if K = $100 and stock is trading $102, then the fwd contract would be cheap with a positive (or negative) value.
** most fwd contracts are constructed with very low initial value.
* note the exp() is applied on the K. When is it applied on the S? [1]
* compare 2 fwd contracts of different strikes?
* fwd contract’s value has delta = 1

[1] A few cases. ATMF options are struck at the fwd price.

sell-side on the FX Vol market

Backgrounder — The traditional meaning of a “sell-side” is basically a player who makes a living
– by commission or
– by earning bid-ask spread (market makers),
– but no insurance premium.
Such a player provides liquidity to the market and seldom consumers liquidity. In so doing they provide a valuable service to the market and are rewarded. In a sense, they sell liquidity.

I now think of fx options as even more like insurance than equity options. There's economic need for fx options. Demand comes from mostly (MNC) corporations. They buy this insurance because they need protection.

Since fx options are insurance, it's natural to classify the participants as sellers and buyers. I guess some big players in this market stay primarily on one side only. (Some banks may need to pay insurance premium just for hedging.) If that's true then the “sell-side” concept can be adjusted to mean players who make a living selling insurance who seldom buys the same insurance except for hedging.

The mainstream sellers are banks. If the interbank bid-ask vol spread is narrow, then these sellers will have little restraint from frequent buying/selling.

Compared to corporations, is there an even bigger category of buyers in the fxo market? I don't think so. I have no statistics, but I believe corporations are the most stable client base for the banks.

I think the commodity options (or options on futures) market isn't that active, but these option sellers are, likewise, insurers to provide for an economic need.

IRS valuation, again

When I see “value of a swap” I first remind myself this is about the value of a series of cash flows, like the combined value of “out $19, in $13, out $2, in $5 …”. This value could be positive or negative. Next I ask myself “value of the cash flows to side 1 or 2”? [1]

A) First, you are always one of A) fixed-receiver or B) float-receiver. I feel for a beginner like me, better focus on one side. [[Hull]] example focuses on the fixed receiver. If IRS is important to your job, you will see both sides so many times and they will become quick and intuitive. From now on, Let’s focus on the fixed receiver.

B) The “position” on our book is valued as a series of cash flows including Inflow and outflow. The valuation calc basically
1) predict the size of each inflow and outflow at each future payment date [1]
2) discounts the net Inflow to PV like $81, -$12, -$25, $52..
3) add up the PV to a single dollar amount like $99

If total inflow PV is positive, then the position is like an asset (as of today). Devil is in the details. For now, step back from the gory details and notice the few important details —

Q: key question (per Kuznetsov) is how to estimate today the rate [1] to be announced in 3 months (by the BBA). It’s not fixed on sign-up but “floating” like the future temperature in Dublin 3 months in the future. How is it estimated?
A: basically use the IR numbers known today to back out (RN?) the 3×9 fwd rate “6M rate 3M forward”. I guess this is like the UIP (not the CIP) — treating the RN expected spot rate as the natural expected spot rate. See http://en.wikipedia.org/wiki/Forward_rate_agreement

Note the very first payment date is fixed, not some “unknown future temperature”. See [[Hull]].

Q: what kinda input data are needed to produce the soft market data which are needed for IRS valuation?
A: Lin Yu pointed out the key soft market data is the libor/swap curve, which often uses Libor, ED Futures , Swap rates from the market. But that’s a bit involved. For now, let’s look at the simple calc in [[Hull]]
A: Libor deposit rates. (A bit tricky!) If valuation-date is denoted T, and the payment dates are T+3M, T+9M .. then we need rate for a loan from T to T+3M.
** I’d say from Libor deposit rates T to T+…., we could estimate all the floating payment.
** note ED future rates are not used in this simple calc.

[1] A minor point — if the value of the cash flows nets to positive for one side, it must be negative for the opposite side.

compound options, basics

Based on P78 [[DerivativeFinancialProducts]].

Most popular Compound option is a call on a put. (I think vanilla Puts are the overall most popular option in Eq and FX, and embedded Calls are the most popular bond options.) Given a lot of buyers are interested in puts, there’s a natural demand for calls-on-puts.

In a Compound option there are 2 layers of fees (i.e. premiums) and 2 expiry dates —

The front fee is what you pay up front to receive the front option. If you exercise front option, you do so by buying the back option, paying the back fee as a 2nd premium to the dealer. Therefore the back fee is a conditional fee.

At end of front option’s lifespan, the back option’s protection period would start. (Remember in this case the back option is a protective put.)

It’s quite common that at end of the front window, the back option has become unnecessary, or back fee has become too expensive given the now reduced risk.

arb between 2 options with K1, K2

It’s not easy to get intuitive feel about arb inequality involving European put/calls of 2 strikes K1 < K2. No stoch or Black/Scholes required. Just use hockey stick diagram i.e. range-of-possibilities payoff diagram.

Essential rule #1 to internalize — if a (super-replicating) portfolio A has terminal value dominating B, then at any time before maturity, A dominates B. Proof? arbitrage. If at any time A is cheaper, we buy A and sell B and keep the profit. At maturity our long A will adequately cover our short B.

—-Q1: Exactly four assets are available: The bond Z with Z0 = $0.9; and three calls. The underlying is not available for you to trade. The calls have identical expiry T, strike K = 20; 22.5; 25, and time-0 price C0(K), where C0(20) = 6.40; C0(22.5) = 4.00; C0(25) = 1.00. Any arbitrage

Consider the portfolio B {long C(22.5) short C(25)} and A {25 Z – 22.5 Z} = {2.5 Z}

At maturity, A is worth $2.5 since the bond has maturity value $1 by definition.
At maturity, B < $2.5, obvious by hockey stick. This is the part to get intuitive with.

By Rule #1, any time before maturity, A should dominate B. In reality, A0 = 2.5 Z0 but B0 = $3 -> arb.

This trick question has some distractive information!

—-Q2: P141 [[xinfeng]] has a (simple) question — put {K=80} is worth $8 and put {K=90} is worth $9. No dividend. Covered on Slide 30 by Roger Lee. Need to remember this rule — 80/90*P(90) should dominates P(80) at time 0 or any time before expiry, otherwise arb.

Consider portfolio A {80/90 units of the K=90 calls} vs B {1 unit of the K=80 call}

If stock finishes above $80 then B = 0 so A >= B i.e. dominates
If stock finishes below $80, then B = 80-S. Hockey stick shows A = 80 – S*80/90 so A dominates.

Therefore at expiration A dominates and by Rule #1 A should be worth more at time 0. In reality, A0=B0.

implied vol vs forecast-realized-vol

In option pricing, we encounter realized vs implied vol (not to be elaborated here). In market risk (VaR etc), we encounter

past-realized-vol vs forecast-realized-vol. Therefore, we have 3 flavors of vol

PP) past realized vol, for a historical period, such as Year 2012

FF) forecast realized vol, for a start/end date range that's after the reference date or valuation date. This valuation date is

typically today.

II) implied vol, for a start/end date range that's after the reference date or valuation date. This valuation date is typically


PP has a straightforward definition, which is basis of FF/II.

Why FF? To assess VaR of a stock (I didn't say “stock option”) over the next 365 days, we need to estimate variation in the stock

price over that period.

FF calculation (whenever you see a FF number) is based on historical data (incidentally the same data underlying PP), whereas II

calculation (whenever you see a II number like 11%) is based on quotes on options whose remaining TTL is being estimated to show an

(annualized) vol of 11%.

See http://www.core.ucl.ac.be/econometrics/Giot/Papers/IMPLIED3_g.pdf compares FF and II.

premium adjusted delta – basic illustration

http://www.columbia.edu/~mh2078/FX_Quanto.pdf says “When computing your delta it is important to know what currency was used to pay the premium. Returning to the stock analogy, suppose you paid for an IBM call option in IBM stock that you borrowed in the stock-lending market. Then I would inherit a long delta position from the option and a short delta position position from the premium payment in stocks. My overall net delta position will still be long (why?), but less long than it would have been if I had paid for it in dollars.”

Suppose we bought an ATM call, so the option position itself gives us +50 delta and let us “control” 100 shares. Suppose premium costs 8 IBM shares (leverage of 12.5). Net delta would be 50-8=42. Our effective exposure is 42%

The long call gives us positive delta (or “positive exposure”) of 50 shares as underlier moves. However, the short stock position reduces that positive delta by 8 shares, so our portfolio is now slightly “less exposed” to IBM fluctuations.

2nd scenario. Say VOD ATM call costs 44 VOD shares. Net delta = 50 – 44 = 6. As underlier moves, we are pretty much insulated — only 6% exposure. Premium-adjusted delta is significantly reduced after the adjustment.

You may wonder why 2nd scenario’s ATM premium is so high. I guess
* either TTL(i.e. expiration) is too far,
* or implied vol is too high,
* or bid ask spread is too big, perhaps due to market domination/manipulation

most popular/important instruments by Singapore banks

I spoke to a derivative market data vendor’s presales. Let’s just say it’s a lady named AA.

Without referring specifically to Singapore market, she said in all banks (i guess she means trading departments) FX is the bread and butter. She said FX desk is the heaviest desk. She said interest rate might be the 2nd most important instrument. Equities and commodities are not …(heavy/active?) among banks.

I feel commercial banks generally like currencies and high quality bonds in favor of equities, unrated bonds and commodities. Worldwide, Commercial banks’ lending business model is most dependent on interest rates. Singapore being an import/export trading hub, its banks have more forex exposure than US or Japanese banks. Their use of credit products is interesting.

AA later cited credit derivative as potentially the 2nd most useful Derivative market data for a typical Singapore bank. (FXVol being the #1). Actually, Most banks don’t trade a lot of credit derivatives, but they need the market data for analysis (like CVA) and risk management. She gave an example — say your bank enters a long-term OTC contract with BNP. You need to assess BNP’s default probability as part of counterparty risk. The credit derivative market data would be relevant. I think the most common is CDS

(Remember this vendor is a specialist in derivative market data.)

The FX desk of most banks make bulk of the money from FXO, not FX spot. She felt spot volume is higher but margin is as low as 0.1 pip, with competition from EBS and other electronic liquidity venues. What she didn’t say is that FXO market is less crowded.

She agreed that many products are moving to the exchanges, but OTC model is more flexible.

RiskReversal -ve bid / +ve ask

Refer to the one-way RR quote in http://bigblog.tanbin.com/2012/06/fx-vol-quoting-convention.html.

Q1: What if 25Delta risk reversal bid/ask quotes are both positive?

As in the above example, dealer (say UBS) gives an RR Ask quote of 3.521%. Let’s say we have some hacker/insider friend to peek at UBS database, and we find the call’s Ask implied-vol is 9.521% and the put’s Bid implied-vol is 6%. In other words, dealer is willing to Write the 25Delta call at an annualized implied-vol of 9% and simultaneously Buy the Put @i-vol of 6%.

Now we ask the same dealer for a bid price. Dealer is bidding 2.8%. Our friend reveals that dealer is secretly willing to Buy the call @i-vol=8.9% (Lower quote) and simultaneously Write the put @i-vol=6.1% (Higher quote).

If you compare the bid vs ask on the call, as market maker the dealer is putting out 2-way quotes to buy low sell high.

If you compare the bid vs ask on the put, as market maker the dealer is putting out 2-way quotes to buy low sell high.

In this scenario, RR bid is below RR ask but both positive.

Q2: Could an RR bid be negative while the ask positive?

Ok We are serious about Selling an RR. To get a better bid price, we ask Dealer2 (SCB) for a Bid quote. Dealer is bidding -0.2%. Our insider tells us this dealer is willing to Buy the call @i-vol=5.9% and simultaneously Write the put @i-vol=6.1%

Between these dealers, Dealer1 would be the best (highest) bid. Now Dealer1 withdraws its quote. Dealer2 is the only bid. Market best RR bid is now negative.

Q2b: When would be RR bid and ask have opposite signs?
A: I guess when the 2 currencies are almost equal in terms of downside/upside

Q3: what if best RR bid and best RR ask are both negative? I think this is the norm in some currency pairs. Suppose market is bearish on the commodity currency (1st) and bullish on the quote currency (2nd). Treating commodity currency as an asset, Sink insurance costs more than surge insurance. Put premium exceeds Call premium. RR would be negative in both bid and ask.

mortgage is like a callable bond, briefly

The mortgage you take on can be, for educational purpose, compared to a personally issued bond (you as issuer) with a predefined monthly repayment and a fixed interest rate. (The floating interest mortgage is comparable to a floating-interest bond.)

When you refinance at a lower interest, it's similar to a callable-bond issuer exercising the call option and then refinance.

The call option is embedded in the “bond”. The call option allows the issuer/borrower to “buy” back the bond from the lender, thereby ending the contract.

back-to-back ccy swap, basics

(see also P198 [[Marki]])


Both Investopedia and Wikipedia authors pick out this one motivation as the main usage of currency swap.

http://www.investopedia.com/terms/c/cross-currency-swap.asp — The reason companies use cross-currency swaps is to take advantage of comparative advantages. For example, if a U.S. company is looking to acquire some yen, and a Japanese company is looking to acquire U.S. dollars, these two companies could perform a swap. The Japanese company likely has better access to Japanese debt markets and could get more favorable terms on a yen loan than if the U.S. company went in directly to the Japanese debt market itself.

Wikipedia has a similiar comment — Another currency swap structure is to combine the exchange of loan principal with an interest rate swap. In such a swap, interest cash flows are not netted before they are paid to the counterparty (as they would be in a vanilla interest rate swap) because they are denominated in different currencies. As each party effectively borrows on the other’s behalf, this type of swap is also known as a back-to-back loan.

Wikipedia article later cites back-to-back as one of the 2 main uses of currency swaps.