Chapter7 Swaps
Nature of Swaps

A swap is an agreement to exchange cash flows
at specified future times according to certain
specified rules
Two popular swaps
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plain vanilla interest rate swaps
fixed-for-fixed currency swaps
7.1 Mechanics of interest rate swaps
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“plain vanilla” interest rate swaps
In this swap a company agrees to pay cash flows
equal to interest at a predetermined fixed rate on
a notional principal for a number of years. In
return, in receives interest at a floating rate on
the same notional principal for the same period of
time.
floating rate
The floating rate in most interest rate swap
agreements is the London Interbank Offered
Rate (LIBOR).
An Example of a “Plain Vanilla” Interest Rate
Swap

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Consider a hypothetical 3-year swap initiated on
March 5,2007,between Microsoft and Intel.
An agreement by Microsoft to receive 6-month
LIBOR & pay a fixed rate of 5% per annum every
6 months for 3 years on a notional principal of
$100 million
Cash Flows to Microsoft
Received:0.5*0.042*100million = 2.1million
Paid:0.5*0.05*100million = 2.5million
Typical Uses of an Interest Rate Swap
Converting a liability from
 fixed rate to floating rate
 floating rate to fixed rate
LIBOR+0.1%→ 5.1%
5.2%→ LIBOR+0.2%
Typical Uses of an Interest Rate Swap
Converting a investment from
 fixed rate to floating rate
 floating rate to fixed rate
4.7%→ LIBOR- 0.3%
LIBOR- 0.2%→ 4.8%
Role of financial institution
Converting a investment from
Role of financial institution
Converting a investment from
Market makers

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Many large financial institutions act as market
makers for swap. They are prepared to enter
swap without having an offsetting swap with
another counterparty.
Market makers must carefully quantify and hedge
the risks they are taking.
Bonds ,FRA ,interest rate futures are example of
the instruments that they can be used for
hedging by swap market makers.

Consider a new swap :
fixed rate = current swap rate
We can reasonably assume that the value of this swap
is zero.
7.2 Day count issues
A LIBOR-based floating-rate cash flow on a swap
payment date is calculated as:
LRn/360
(L : principal ,R : relevant LIBOR rate n : the
number of day since the last payment date)
7.3 Confirmation
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A confirmation is the legal agreement underlying
a swap and is signed by representatives.
International Swap and Derivatives Association
(ISDA) in New York.
The confirmation specifies that the following
business day convention is to be used and that
the US calendar determines which days are
business days and which are holiday.
7.4 The comparative-advantage argument


An explanation commonly put forward to explain the
popularity of swaps concerns comparative advantage.
AAA Corp wants to borrow floating
BBB Corp wants to borrow fixed
a – b = Δ Fixed – Δ Floating rate
= 1.2% - 0.7%
= 0.5 %
Pay LIBOR – 0.35%
Pay 4.95%
Swap
AAA Corp : gain 0.23%
BBB Corp : gain 0.23%
FI : 0.04%
Total :0.5%
Criticism of the Comparative Advantage Argument
 The 4.0% and 5.2% rates available to AAA Corp and
BBB Corp in fixed rate markets are 5-year rates.
 The LIBOR−0.1% and LIBOR+0.6% rates available in
the floating rate market are six-month rates.
 BBB Corp’s fixed rate depends on the spread above
LIBOR it borrows at in the future.
7.5 The Nature of Swap Rates
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Six-month LIBOR is a short-term AA borrowing rate.
The 5-year swap rate has a risk corresponding to the
situation where 10 six-month loans are made to AA
borrowers at LIBOR.
This is because the lender can enter into a swap
where income from the LIBOR loans is exchanged for
the 5-year swap rate.
7.6 Determining LIBOR/Swap zero rates
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Consider a new swap where the fixed rate is the swap
rate .
When principals are added to both sides on the final
payment date the swap is the exchange of a fixed rate
bond for a floating rate bond .
The floating-rate rate bond is worth par. The swap is
worth zero. The fixed-rate bond must therefore also
be worth par.
This shows that swap rates define par yield bonds
that can be used to bootstrap the LIBOR (or
LIBOR/swap) zero curve.
Coupon rate : 5%
→Gain $2.5 (100*0.5*5%) semiannually
7.6 Valuation of interest rate swaps
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Interest rate swaps can be valued as the difference
between the value of a fixed-rate bond and the value
of a floating-rate bond
Alternatively, they can be valued as a portfolio of
forward rate agreements (FRAs)
Valuation in Terms of Bonds
Form a point of view of the floating-rate payer
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The fixed rate bond is valued in the usual way.
The floating rate bond is valued by noting that it is
worth par immediately after the next payment date.
Valuation in Terms of FRAs
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Each exchange of payments in an interest rate
swap is an FRA.
The FRAs can be valued on the assumption that
today’s forward rates are realized.

The fixed rate in an interest rate swap is chosen
so that the swap is worth zero initially. This
means that at the outset of a swap the sum of
the values of the FRAs underlying the swap is
zero.
7.8 Currency swaps

In its simplest from ,this involves exchanging
principal and interest payments in one currency
for principal and interest payments in another.
Typical Uses of a Currency Swap


Conversion from a liability in one currency to a
liability in another currency
Conversion from an investment in one currency
to an investment in another currency
Comparative Advantage
General Electric wants to borrow AUD
Qantas wants to borrow USD
7.9 Valuation of Currency Swaps

Like interest rate swaps, currency swaps can be
valued either as the difference between 2 bonds
or as a portfolio of forward contracts.
Valuation in Terms of Forwards
Swaps & Forwards


A swap can be regarded as a convenient way of
packaging forward contracts.
Although the swap contract is usually worth zero
at the outset, each of the underlying forward
contracts are not worth zero.
7.10 Credit Risk
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A swap is worth zero to a company initially.
At a future time its value is liable to be either
positive or negative.
The company has credit risk exposure only
when its value is positive.
Some swaps are more likely to lead to credit
risk exposure than others.
What is the situation if early forward rates have
a positive value?
What is the situation when the early forward
rates have a negative value?
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7.11 Other Types of Swaps
•
Floating-for-floating interest rate swaps,
amortizing swaps, step up swaps, forward swaps,
constant maturity swaps, compounding swaps,
LIBOR-in-arrears swaps, accrual swaps, diff
swaps, cross currency interest rate swaps, equity
swaps, extendable swaps, puttable swaps,
swaptions, commodity swaps, volatility
swaps……..
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The End