An
interest rate swap is a derivative in which one party exchanges a stream
of interest payments for another party's stream of cash flows.
Interest rate swaps can be used by hedgers to manage their fixed
or floating assets and liabilities. They can also be used by
speculators to replicate unfunded bond exposures to profit from
changes in interest rates. As such, interest rate swaps are
very popular and highly liquid instruments.
Structure
In an interest
rate swap, each counterparty agrees to pay either a fixed or
floating rate denominated in a particular currency to the other
counterparty. The fixed or floating rate is multiplied by a
notional principal amount (say, USD 1 million). This notional
amount is generally not exchanged between counterparties, but
is used only for calculating the size of cashflows to be exchanged.
The most
common interest rate swap is one where one counterparty pays
a fixed rate (the swap rate) while receiving a floating rate
(usually pegged to LIBOR). Consider the following swap in which
Party A agrees to pay Party B periodic interest rate payments
of LIBOR + 50 bps (0.50%) in exchange for periodic interest
rate payments of 3.00%. Note that there is no exchange of the
principal amounts and that the interest rates are on a "notional"
(i.e. imaginary) principal amount. Also note that the interest
payments are settled in net (e.g. if LIBOR + 50 bps is 1.20%
then Party A receives 1.80% and Party B pays 1.80%). The fixed
rate (3.00% in this example) is referred to as the swap rate.^{[1]}
At the point
of initiation of the swap, the swap is priced so that it has
a net present value of zero. If one party wants to pay 50 bps
above the par swap rate, the other party has to pay approximately
50 bps over LIBOR to compensate for this.
Types
Being OTC
instruments interest rate swaps can come in a huge number of
varieties and can be structured to meet the specific needs of
the counterparties. That said, by far the most common are fixedforfixed,
fixedforfloating or floatingforfloating. The legs of the
swap can be in the same currency or in different currencies.
(A singlecurrency fixedforfixed rate swap is generally not
possible; since the entire cashflow stream can be predicted
at the outset there would be no reason to maintain a swap contract
as the two parties could just settle for the difference between
the present values of the two fixed streams, the only exceptions
would be where the notional amount on one leg is uncertain or
other esoteric uncertainty is introduced)
Fixedforfloating
rate swap, same currency
Party P
pays/receives fixed interest in currency A to receive/pay floating
rate in currency A indexed to X on a notional N for a tenor
T years. For example, you pay fixed 5.32% monthly to receive
USD 1M Libor monthly on a notional USD 1 million for 3 years.
The party that pays fixed and receives floating coupon rates
is said to be long the interest swap.
Fixedforfloating
swaps in same currency are used to convert a fixed rate asset/liability
to a floating rate asset/liability or vice versa. For example,
if a company has a fixed rate USD 10 million loan at 5.3% paid
monthly and a floating rate investment of USD 10 million that
returns USD 1M Libor +25 bps monthly, it may enter into a fixedforfloating
swap. In this swap, the company would pay a floating USD 1M
Libor+25 bps and receive a 5.5% fixed rate, locking in 20bps
profit.
Fixedforfloating
rate swap, different currencies
Party P
pays/receives fixed interest in currency A to receive/pay floating
rate in currency B indexed to X on a notional N at an initial
exchange rate of FX for a tenure of T years. For example, you
pay fixed 5.32% on the USD notional 10 million quarterly to
receive JPY 3M (JIBOR) monthly on a JPY notional 1.2 billion
(at an initial exchange rate of USDJPY 120) for 3 years. For
nondeliverable swaps, the USD equivalent of JPY interest will
be paid/received (according to the FX rate on the FX fixing
date for the interest payment day). No initial exchange of the
notional amount occurs unless the Fx fixing date and the swap
start date fall in the future.
Fixedforfloating
swaps in different currencies are used to convert a fixed rate
asset/liability in one currency to a floating rate asset/liability
in a different currency, or vice versa. For example, if a company
has a fixed rate USD 10 million loan at 5.3% paid monthly and
a floating rate investment of JPY 1.2 billion that returns JPY
1M Libor +50 bps monthly, and wants to lock in the profit in
USD as they expect the JPY 1M Libor to go down or USDJPY to
go up (JPY depreciate against USD), then they may enter into
a FixedFloating swap in different currency where the company
pays floating JPY 1M Libor+50 bps and receives 5.6% fixed rate,
locking in 30bps profit against the interest rate and the fx
exposure.
Floatingforfloating
rate swap, same currency
Party P
pays/receives floating interest in currency A Indexed to X to
receive/pay floating rate in currency A indexed to Y on a notional
N for a tenor T years. For example, you pay JPY 1M Libor monthly
to receive JPY 1M Tibor monthly on a notional JPY 1 billion
for 3 years.
Floatingforfloating
rate swaps are used to hedge against or speculate on the spread
between the two indexes widening or narrowing. For example,
if a company has a floating rate loan at JPY 1M Libor and the
company has an investment that returns JPY 1M Tibor+30 bps and
currently the JPY 1M Tibor = JPY 1M Libor +10bps. At the moment,
this company has a net profit of 40 bps. If the company thinks
JPY 1M tibor is going to come down or JPY 1M Libor is going
to increase in the future and wants to insulate from this risk,
they can enter into a Float float swap in same currency where
they pay JPY TIBOR +10 bps and receive JPY LIBOR+35 bps. with
this, they have effectively locked in a 15 bps profit instead
of running with a current 40 bps gain and index risk. The 5bps
difference comes from the swap cost which includes the market
expectations of the future rates in these two indices and the
bid/offer spread which is the swap commission for the swap dealer.
Floatingforfloating
rate swaps are also seen where both sides reference the same
index, but on different payment dates, or use different business
day conventions. These have almost no use for speculation, but
can be vital for assetliability management. An example would
be swapping 3M Libor being paid with prior nonbusiness day
convention, quarterly on JAJO (i.e. Jan, Apr, Jul, Oct) 30,
into FMAN (i.e. Feb, May, Aug, Nov) 28 modified following.
Floatingforfloating
rate swap, different currencies
Party P
pays/receives floating interest in currency A indexed to X to
receive/pay floating rate in currency B indexed to Y on a notional
N at an initial exchange rate of FX for a tenor T years. For
example, you pay floating USD 1M Libor on the USD notional 10
million quarterly to receive JPY 3M Tibor monthly on a JPY notional
1.2 billion (at an initial exchange rate of USDJPY 120) for
4 years.
To explain
the use of this type of swap, consider a US company operating
in Japan. To fund their Japanese growth, they need JPY 10 billion.
The easiest option for the company is to issue debt in Japan.
As the company might be new in the Japanese market without a
well known reputation among the Japanese investors, this can
be an expensive option. Added on top of this, the company might
not have appropriate debt issuance program in Japan and they
might lack sophisticated treasury operation in Japan. To overcome
the above problems, it can issue USD debt and convert to JPY
in the FX market. Although this option solves the first problem,
it introduces two new risks to the company:
 FX risk.
If this USDJPY spot goes up at the maturity of the debt, then
when the company converts the JPY to USD to pay back its matured
debt, it receives less USD and suffers a loss.
 USD and
JPY interest rate risk. If the JPY rates come down, the return
on the investment in Japan might go down and this introduces
an interest rate risk component.
The first
exposure in the above can be hedged using long dated FX forward
contracts but this introduces a new risk where the implied rate
from the FX spot and the FX forward is a fixed rate but the
JPY investment returns a floating rate. Although there are several
alternatives to hedge both the exposures effectively without
introducing new risks, the easiest and the most cost effective
alternative would be to use a floatingforfloating swap in
different currencies. In this, the company raises USD by issuing
USD Debt and swaps it to JPY. It receives USD floating rate
(so matching the interest payments on the USD Debt) and pays
JPY floating rate matching the returns on the JPY investment.
Fixedforfixed
rate swap, different currencies
Party P
pays/receives fixed interest in currency A to receive/pay fixed
rate in currency B for a term of T years. For example, you pay
JPY 1.6% on a JPY notional of 1.2 billion and receive USD 5.36%
on the USD equivalent notional of 10 million at an initial exchange
rate of USDJPY 120.
Other
variations
A number
of other variations are possible, although far less common.
Mostly tweaks are made to ensure that a bond is hedged "perfectly",
so that all the interest payments received are exactly offset
by the swap. This can lead to swaps where principal is paid
on one or more legs, rather than just interest (for example
to hedge a coupon strip), or where the balance of the swap is
automatically adjusted to match that of a prepaying bond (such
as RMBS).
Uses
Interest
rate swaps were originally created to allow multinational companies
to evade exchange controls. Today, interest rate swaps are used
to hedge against or speculate on changes in interest rates.
Hedging
Today, interest
rate swaps are often used by firms to alter their exposure to
interestrate fluctuations, by swapping fixedrate obligations
for floating rate obligations, or vice versa. By swapping interest
rates, a firm is able to alter its interest rate exposures and
bring them in line with management's appetite for interest rate
risk. For example, Fannie Mae uses interest rate derivatives to
hedge its cash flows. The products it uses are payfixed swaps,
receivefixed swaps, basis swaps, interest rate cap and swaptions,
and forward starting swaps. Its "cash flow hedges" had a notional
value of $872 billion at December 31, 2003, while its "fair value
hedges" stood at $169 billion (SEC Filings) (2003 10K page 79).
Its "net value" on "a net present value basis, to settle at current
market rates all outstanding derivative contracts" was (7,712)
million and 8,139 million, which makes a total of 6,633 million
when a "purchased options time value" of 8,139 million is added.
What Fannie
Mae doesn't want is for example a wide "duration gap" for a
long period. If rates turn the opposite way on a duration gap
the cash flow from assets and liabilities may not match, resulting
in inability to pay the bills on liabilities. It reports the
duration gap regularly in its (8K Regulation FD Disclosure),
see earlier 10K's for charts and more information (Investor
Relations: Annual Reports & Proxy Statements). (Dec 1999
 Dec 2002 duration gap), (2003 gap).
Speculation
Interest
rate swaps are also used speculatively by hedge funds or other
investors who expect a change in interest rates or the relationships
between them. Traditionally, fixed income investors who expected
rates to fall would purchase cash bonds, whose value increased
as rates fell. Today, investors with a similar view could enter
a floatingforfixed interest rate swap; as rates fall, investors
would pay a lower floating rate in exchange for the same fixed
rate.
Interest
rate swaps are also very popular due to the arbitrage opportunities
they provide. Due to varying levels of creditworthiness in companies,
there is often a positive quality spread differential which
allows both parties to benefit from an interest rate swap.
The interest
rate swap market is closely linked to the Eurodollar futures
market which trades at the Chicago Mercantile Exchange.
Valuation
and pricing
The present
value of a plain vanilla (i.e. fixed rate for floating rate)
swap can easily be computed using standard methods of determining
the present value (PV) of the fixed leg and the floating leg.
The value
of the fixed leg is given by the present value of the fixed
coupon payments known at the start of the swap, i.e.

where C
is the swap rate, M is the number of fixed payments,
P is the notional amount, t_{i}
is the number of days in period i, T_{i}
is the basis according to the day count convention and df_{i}
is the discount factor.
Similarly,
the value of the floating leg is given by the present value
of the floating coupon payments determined at the agreed dates
of each payment. However, at the start of the swap, only the
actual payment rates of the fixed leg are known in the future,
whereas the forward rates (derived from the yield curve) are
used to approximate the floating rates. Each variable rate payment
is calculated based on the forward rate for each respective
payment date. Using these interest rates leads to a series of
cash flows. Each cash flow is discounted by the zerocoupon
rate for the date of the payment; this is also sourced from
the yield curve data available from the market. Zerocoupon
rates are used because these rates are for bonds which pay only
one cash flow. The interest rate swap is therefore treated like
a series of zerocoupon bonds. Thus, the value of the floating
leg is given by the following:

where N
is the number of floating payments, f_{j}
is the forward rate, P is the notional amount, t_{j}
is the number of days in period j, T_{j}
is the basis according to the day count convention and df_{j}
is the discount factor. The discount factor always starts with
1. The discount factor is found as follows:
 [Discount
factor in the previous period]/[1 + (Forward rate of the floating
underlying asset in the previous period Ã— Number of days
in period/360)].
The fixed
rate offered in the swap is the rate which values the fixed
rates payments at the same PV as the variable rate payments
using today's forward rates, i.e.:
 ^{[2]}
Therefore,
at the time the contract is entered into, there is no advantage
to either party, i.e.,

Thus, the
swap requires no upfront payment from either party.
During the
life of the swap, the same valuation technique is used, but
since, over time, the forward rates change, the PV of the variablerate
part of the swap will deviate from the unchangeable fixedrate
side of the swap. Therefore, the swap will be an asset to one
party and a liability to the other. The way these changes in
value are reported is the subject of IAS 39 for jurisdictions
following IFRS, and FAS 133 for U.S. GAAP. Swaps are marked
to market by debt security traders to visualize their inventory
at a certain time.
Risks
Interest
rate swaps expose users to interest rate risk and credit risk.
 Interest
rate risk originates from changes in the floating rate. In
a plain vanilla fixedforfloating swap, the party who pays
the floating rate benefits when rates fall. (Note that the
party that pays floating has an interest rate exposure analogous
to a long bond position.)
 Credit
risk on the swap comes into play if the swap is in the money
or not. If one of the parties is in the money, then that party
faces credit risk of possible default by another party. This
is true for all swaps where there is no exchange of principal.
Market
size
The Bank
for International Settlements reports that interest rate swaps
are the largest component of the global OTC derivative market.
The notional amount outstanding as of December 2006 in OTC interest
rate swaps was $229.8 trillion, up $60.7 trillion (35.9%) from
December 2005. These contracts account for 55.4% of the entire
$415 trillion OTC derivative market. However, interest rate
swaps are not standardized enough to allow them to be traded
through a futures exchange like an option or a futures contract.
References
 "Interest Rate Swap" by Fiona Maclachlan, The Wolfram
Demonstrations Project.
 Understanding interest rate swap math & pricing. California
Debt and Investment Advisory Commission (200701). Retrieved
on 20070927.
 Pricing
and Hedging Swaps, Miron P. & Swannell P., Euromoney books
1991
External
links