Interest Rate Swaps:
Overview
FINC 456
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
value.
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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
market…
$60 trillion dollars notional outstanding/ IRS are about 40%…
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Describing Interest Rate Swaps
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Interest rate swaps can be described by:
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Term sheets (contract specifications)
Cashflows/Inflow-outflow diagrams
“swap boxes”
exposure diagrams
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%) semiannually for 10 years.
The cash amount of payments is calculated by applying
the rates to some notional amount.
Interest Rate Swaps: Mechanics
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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)
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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
basis


The floating side, with R as the forward rate is:

floating paymentt +1 = Q × Rt ×  days
basis 

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Interest Rate Swap: Mechanics, con’t
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So at each payment date, the net cashflow is

Cashflowt = Q × ( F − Rt −1 ) ×  days
basis


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.
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If interest rates are projected to rise, swaps provide a lowcost 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.
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Interest Rate Swaps: Term Sheet
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Receiving: 6M LIBOR
Paying: 6.25%
Notional: 100M
Maturity: February 13, 2011
Periodicity: Semi-annual, normal reset
Basis: Actual/360
Interest Rate Swap Cashflows
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For example, a 5 year, $100 MM notional swap,
paying fixed and receiving floating could be
depicted as:
15-Aug-01
15-Feb-02
15-Aug-02
15-Feb-03
15-Aug-03
15-Feb-04
15-Aug-04
15-Feb-05
15-Aug-05
15-Feb-06
Projected
Floating Rates Fixed Rate
5.75%
6.01%
5.80%
6.01%
5.85%
6.01%
5.90%
6.01%
5.95%
6.01%
6.00%
6.01%
6.10%
6.01%
6.20%
6.01%
6.30%
6.01%
6.40%
6.01%
PV
$
$
$
$
$
$
$
$
$
$
(floating)
2,794,654
2,739,509
2,684,601
2,629,963
2,575,626
2,521,621
2,487,771
2,452,526
2,415,979
2,378,225
PV (fixed) Net Payment
(125,208)
$ 2,919,862
(98,063)
$ 2,837,572
(72,331)
$ 2,756,932
(47,970)
$ 2,677,933
(24,941)
$ 2,600,566
(3,201)
$ 2,524,821
37,677
$ 2,450,094
76,101
$ 2,376,424
112,126
$ 2,303,853
145,809
$ 2,232,416
FV
1.0288
1.0586
1.0895
1.1217
1.1551
1.1897
1.2260
1.2640
1.3038
1.3455
PV
0.9721
0.9447
0.9178
0.8915
0.8658
0.8405
0.8157
0.7911
0.7670
0.7432
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Interest Rate Swaps: “Swap Boxes”
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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
LIBOR+spread (200 bp)
Bondholders
Valuing Interest Rate Swaps
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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).
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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.
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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.
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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:
Generalizations
❑
Interest rate swaps are extremely customizable and
have spawned a near infinite family of products.
All types of indices…Treasury, LIBOR, Prime, CP, etc.
Payments in different currencies
Used to closely match operational exposures
To take advantage of financing opportunities (recently, in
Japan)
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
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