Interest Rate Swaps:
Interest Rate Swaps
❑ In general, a swap is a contract specifying the exchange in
the future of one cashflow for another. The amount of the
cashflow usually depends on the movement of some market
Swaps are pervasive in nearly all markets, primarily currency,
commodity, and interest rates, but also (more exotically) in
equity, credit and such things as weather.
All that is typically required is that both counterparties agree to
when and how the cashflows will be set and paid.
❑ An interest rate swap involves the periodic exchange of
cashflows linked to interest rates.
❑ Interest rate swaps dominate the interest rate derivative
$60 trillion dollars notional outstanding/ IRS are about 40%…
Describing Interest Rate Swaps
❑ Interest rate swaps can be described by:
Term sheets (contract specifications)
❑ Interest rate swaps most commonly involve one
party paying a fixed interest rate and the other
party paying a floating interest rate.
For example 6M LIBOR vs. fixed (I.e. 6.25%) semi-
annually for 10 years.
The cash amount of payments is calculated by applying
the rates to some notional amount.
Interest Rate Swaps: Mechanics
❑ For the standard (plain vanilla) interest rate swap,
one party pays a fixed rate, and the other pays a
floating rate, linked to some index (usually LIBOR)
Each payment stream is called a leg of the swap…
❑ The payment on the fixed rate leg is easy to
calculate, where the notional is Q, and the F is the
fixed swap rate: fixed payment = Q × F × days
❑ The floating side, with R as the forward rate is:
floating paymentt +1 = Q × Rt × days
Interest Rate Swap: Mechanics, con’t
❑ So at each payment date, the net cashflow is
Cashflowt = Q × ( F − Rt −1 ) × days
❑ Question: from whose perspective is this cashflow?
By convention, long swaps pay fixed and receive floating…
So a short swap pays floating and receives fixed.
❑ Note that the index interest rate (think LIBOR here)
is set at the beginning of the period, and the payment
is realized at the end.
This is exactly the way that floating rate bonds/loans work
Interest Rate Swaps: Common uses
❑ Corporations employ interest rate swaps to
dynamically change their financing structure from
floating rate exposure to fixed, and vice versa.
If interest rates are projected to rise, swaps provide a low-
cost method to lock in current rates.
If interest rates are projected to fall, swaps can allow
corporations to take advantage of the lower financing costs.
❑ Swaps can also more precisely match financing risks
with operational risks.
❑ Swaps can be used to lengthen or shorten the
average maturity of a portfolio or liability structure.
Interest Rate Swaps: Term Sheet
❑ Receiving: 6M LIBOR
❑ Paying: 6.25%
❑ Notional: 100M
❑ Maturity: February 13, 2011
❑ Periodicity: Semi-annual, normal reset
❑ Basis: Actual/360
Interest Rate Swap Cashflows
❑ For example, a 5 year, $100 MM notional swap,
paying fixed and receiving floating could be
Floating Rates Fixed Rate PV (floating) PV (fixed) Net Payment FV PV
15-Aug-01 5.75% 6.01% $ 2,794,654 $ 2,919,862 (125,208) 1.0288 0.9721
15-Feb-02 5.80% 6.01% $ 2,739,509 $ 2,837,572 (98,063) 1.0586 0.9447
15-Aug-02 5.85% 6.01% $ 2,684,601 $ 2,756,932 (72,331) 1.0895 0.9178
15-Feb-03 5.90% 6.01% $ 2,629,963 $ 2,677,933 (47,970) 1.1217 0.8915
15-Aug-03 5.95% 6.01% $ 2,575,626 $ 2,600,566 (24,941) 1.1551 0.8658
15-Feb-04 6.00% 6.01% $ 2,521,621 $ 2,524,821 (3,201) 1.1897 0.8405
15-Aug-04 6.10% 6.01% $ 2,487,771 $ 2,450,094 37,677 1.2260 0.8157
15-Feb-05 6.20% 6.01% $ 2,452,526 $ 2,376,424 76,101 1.2640 0.7911
15-Aug-05 6.30% 6.01% $ 2,415,979 $ 2,303,853 112,126 1.3038 0.7670
15-Feb-06 6.40% 6.01% $ 2,378,225 $ 2,232,416 145,809 1.3455 0.7432
Interest Rate Swaps: “Swap Boxes”
❑ Swaps are often described by using boxes to
represent counterparties and flows
Note: this doesn’t give any information about the
frequency of flows
Fixed (Swap) Rate
Corporation Swap Dealer
LIBOR+spread (200 bp)
Valuing Interest Rate Swaps
❑ The swap (fixed) rate is usually set so that the
present value of both sides of the swap equal zero.
❑ A swap can be thought of as the interest payments
due from borrowing at a floating rate and lending at
a fixed rate (or vice versa).
Another way of stating this: a swap is a portfolio of a
coupon bond and a floating-rate note (FRN).
❑ The paying fixed side of a swap gains value if
interest rates rise; it loses value when rates fall.
Interest Rate Swaps:
A word about credit
❑ Swap “books” (that is, the total swap position of a
bank) are often far in excess of the bank’s capital,
on a notional basis.
What are the credit risks associated with swaps?
Are they similar to corresponding bond transactions?
How might correlation factor into this?
❑ To mitigate concerns, banks often set up AAA
subsidiaries to transact their swaps.
Interest Rate Swaps:
❑ Interest rate swaps are extremely customizable and
have spawned a near infinite family of products.
All types of indices…Treasury, LIBOR, Prime, CP, etc.
Used to closely match operational exposures
Payments in different currencies
To take advantage of financing opportunities (recently, in
Match financing with expenditures for multinationals
Notional amounts that accrete/amortize, or are linked to
other market quantities
Frequently found in mortgage/financing related industries
where pre-payments are possible