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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 plain vanilla interest rate swaps fixed-for-fixed currency swaps. 7.1 Mechanics of interest rate swaps.

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Chapter7 Swaps

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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

  • plain vanilla interest rate swaps

  • fixed-for-fixed currency swaps

7.1 Mechanics of interest rate swaps

  • “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

  • 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

Converting a liability from

  • fixed rate to floating rate

  • floating rate to fixed rate

Typical Uses of an Interest Rate Swap

LIBOR+0.1%→ 5.1%

5.2%→ LIBOR+0.2%

Converting a investment from

  • fixed rate to floating rate

  • floating rate to fixed rate

Typical Uses of an Interest Rate Swap

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

  • 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:


(L : principal ,R : relevant LIBOR rate n : the number of day since the last payment date)

7.3 Confirmation

  • 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%


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

  • 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

  • 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

  • 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

  • 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

  • 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 Valuationof 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

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?


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……..


The End

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