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.

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.

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.

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.

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.

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, …

valuation of existing IR swap – example

Based on (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.

##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.

treat IRS floating cashflow "stream" as a commodity

In FX, it’s extremely useful to think of first currency as some kind of commodity like silver… Similarly, in IRS, it’s useful to treat the floating Income stream as a commodity (like silver).

You as the IR “Swap buyer” agrees to pay a fixed price in fixed installments. In exchange you receive something of changing value — whose market value changes daily. Suppose we enter a vanilla IRS to receive floating. When we put down the phone with counter-party, we have agreed to pay a fixed (for eg.) 3.4% price for a “silver” in the form of a stream of floating coupons. This is a bit similar to buying an annuity.

The 3.4% fixed rate is like an execution price on the exchange. Next hour (day), the same silver could fetch more, so another buyer would execute the trade at a higher price, like 3.42%, so my existing position would have a positive PnL. This simplified view assumes a null discount rate of 0 (or equivalently, a discount factor of 1.0).

The changing market value of the “silver” we bought is tied to Libor. We “long” for Libor to rise –We are long Libor, as we are long silver.

On the other hand, if you are a dealer selling IRS, you are short Libor as you are short silver.

By comparison, if you write put/call contracts, you are short volatility. Intuitively, consider OTM — lower vol reduces the chance of option finishing ITM, so you are more likely to pocket the premium. As a fire insurer, lower vol means lower chance of fire disaster — good for you the insurer.

I hope this helps beginners get a “feel” of the terminology in IRS.

vega of a vanilla IRS@@

Q: if Libor interest rate volatility moves by a tiny bit (for eg from 22% to 22.1%), how much would a long IRS position’s current PnL change?  To keep things simple, consider a IRS with a single payment at the end of 2013.

Jargon — Long position is the fixed-payer’s position, who stands to receive the floating payments. See

%%A: I feel this is similar to a long position in Gold futures. You have already agreed to pay a fixed price of $9000 for the asset. The asset you have bought may have a market value higher or lower today, tomorrow and and on delivery date. Futures exchange uses end-of-day mark to market to issue margin calls… Very familiar.

Now, how about vega? I feel a Gold future has no vega. I think it’s delta-1. When the Implied[1] vol of gold moves from 22% to 22.1%, the gold futures position doesn’t undergo a definite amount of MV change. It can dip or surge or stay flat.

Similarly, I would assume an IRS long position has no vega.

[1] Note vega is measured against Implied vol, not realized vol.

IRS trading in a big IR Swap dealer

A3: each deal is tailor made for a particular client. A deal (or a “trade”) often has more than 100 attributes and a lifecycle of its own.

I spoke with a big US investment bank (Citi?) and a big European bank. IRS is a dealer market — No exchanges; each dealer takes positions. (There’s London Clearing House though). Each dealer bank maintains bid/offer but don’t publish them. Why? See A3. Each new client is signed on by an elaborate on-boarding/account-opening process, through the bank’s dedicated sales team. I guess that’s the signing of ISDA Master Agreement.

Once signed up, a client can send an RFQ with a deal size but without a price and without a Buy/Sell indicator. Bank typically responds with a fully disclosed bid/offer price pair. Client can either hit the bid or lift the offer.

Since IRS trade size is much larger than equities, the daily volume of trades is much smaller.

A dealer bank maintains IRS bid/offer pairs in multiple currencies. But here we are talking about single-currency swap.

There are dealers in cross-currency IRS, but that’s a different market.

IR drv trading system

IRS is the primary product in an IRD desk.

Major components of an IRD trading system – 1) booking/capture (b/c), 2) Risk/PnL. Actually, Risk is not a desk-specific system. Rather, deal pricing/risk analytics system is cross-asset and covers IRD, bonds, structured products, FX, and used to cover Credit.

B/C is the primary app for traders. For strategists, primary app is pricing/risk system (c++). For operations users, B/C offers STP confirms and settlement i.e. periodic payments.

B/C system actually expands to cover the full life cycle of a deal – resets, assignments, unwinds

Key object is a trade or a deal or contract. Firmwide risk engine and pricing engine (for IRS bids/offers) need these “positions”. For real time risk and real_time_pricing, all deals need fast processing.

%Q: 2nd biggest product after IRS?
A: FRA, but we also trade cross-currency swaps, swaptions, caps/floors
A: There are flow IRD deals and exotic, “structured” instruments. Exotics are low volume, high margin. But momentum is in the flow business — Growing volume. Arms race.

Even the commonplace contract in the flow business could be more complex than a stock/bond trade. Customer wants a tailor-made deal , so deal is complex – with 100+ attributes, compared to 20+ for trades by other desks.

IRS has no secondary market. The only way to get out of a contract is unwind.

There’s regulatory pressure to clear IRS through a clearing house, possibly CME.

There’s close link btw Treasury desk and IRS desk. When trader takes a T position, she (tries to?) immediately enters an IRS deal.

Flow IRD Margin is better than Treasuries and FX, and trade volume is lower.

IRD Contracts with collateral and margin might become more widespread when IRS gets standardized with a central clearing house. Right now, some of these contracts have daily revaluation and daily settlement, but in a separate margin account.

%Q: 24-hour?
A: no. Users sit in US, Europe, Asia, South America but NY is the last office to close the day.

IRS pricing <- forward <- spot rate

I don’t think this needs a real trading system. low volume, simple math

Pricing a swap is all about predicting actual floating payments or future libor[4] rates or forward rates at each quarterly reset date.

[4] For muni, libor is replaced by the SIFMA muni swap index illustrates derivation of a single forward rate from a series of spot rates. “forward rate is a prediction about future spot rates.”

1) all the spot rates of ED deposits (not futures)
2) market (forward) rates of ED futures,
those future libor rates on each quarterly reset date are solvable. This is the basis of floating payment estimation.

In fact, “expected” 3m libor rate on each quarter boundary date (IMM date) is published in eurodollar futures  market[1]. Therefore the derivation is IRS pricing <- forward rates <- ED CD rates + ED futures rates. Note the floating leg comprises periods (aka coupon period). Pay at end of period but payment amount reset at onset of period. See also post on discount curve.

[1] ED futrures rates are very different from the deposit rates announced by BBA. There’s no “market” for deposit rate.

What If I am convinced 3m USD libor will hit 120 bps/yr on 1/1/2020 but the derived libor is 200 bps/yr? How do i lock in the 1.2%? Well, the relevant eurodollar futures contract is trading at 98. I would buy it and hope it becomes 99.