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

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 vs FX loans – popularity – off balance sheet

(labels – FX)

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 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 would tie up too much capital – capital inefficiency. Even for the client (IBM), I feel borrowing would often require collaterals.

FX swap in contrast requires much less capital.

A different form of IRS off-balance-sheet benefit is given in, applicable for a buy-side as well.

currency risk in FX swap vs forward outright

(labels – FX)

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 base 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”.

GC tuning: will these help@@

Q: have a small nursery generation, so as to increase the frequency of GC collections?

AA: An optimal nursery size for maximum application throughput is such that as many objects as possible are garbage collected by young collection rather than old collection. This value approximates to about half of the free heap.

Q: have maximum heap size exceeding RAM capacity.
A: 32-bit JVM won’t let you specify more than 4G even with 32 GB RAM. Suppose you use 64-bit JVM, then actually JVM would start and would likely use up all available RAM and starts paging.