ch 07 hull fundamentals 7 the d

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Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010

Swaps

Chapter 7

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Nature of Swaps

A swap is an agreement toexchange cash flows at specifiedfuture times according to certainspecified rules

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An Example of a Plain Vanilla

Interest Rate Swap

An agreement by Microsoft to receive6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3years on a notional principal of $100millionNext slide illustrates cash flows

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---------Millions of Dollars---------

LIBOR FLOATING FIXED Net

Date Rate Cash Flow Cash Flow Cash Flow

Mar.5, 2010 4.2%Sept. 5, 2010 4.8% +2.10 2.50 0.40

Mar.5, 2011 5.3% +2.40 2.50 0.10

Sept. 5, 2011 5.5% +2.65 2.50 +0.15

Mar.5, 2012 5.6% +2.75 2.50 +0.25

Sept. 5, 2012 5.9% +2.80 2.50 +0.30

Mar.5, 2013 6.4% +2.95 2.50 +0.45

Cash Flows to Microsoft(See Table 7.1, page 159

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Typical Uses of an

Interest Rate SwapConverting a liability from

fixed rate to floating ratefloating rate to fixed rate

Converting an investment fromfixed rate to floating ratefloating rate to fixed rate

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Intel and Microsoft (MS)Transform a Liability(Figure 7.2, page 160)

Intel MS

LIBOR

5%

LIBOR+0.1%

5.2%

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Financial Institution is Involved(Figure 7.4, page 162)

F.I.

LIBOR LIBOR

LIBOR+0.1%

4.985% 5.015%

5.2%Intel MS

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Intel and Microsoft (MS)Transform an Asset(Figure 7.3, page 161)

Intel MS

LIBOR

5%

LIBOR-0.2%

4.7%

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Financial Institution is Involved(See Figure 7.5, page 163)

Intel F.I. MS

LIBOR LIBOR

4.7%

5.015%4.985%

LIBOR-0.2%

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Quotes By a Swap Market Maker(Table 7.3, page 163)

Maturity Bid (%) Offer (%) Swap Rate (%)2 years 6.03 6.06 6.045

3 years 6.21 6.24 6.225

4 years 6.35 6.39 6.370

5 years 6.47 6.51 6.490

7 years 6.65 6.68 6.66510 years 6.83 6.87 6.850

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The Comparative AdvantageArgument (Table 7.4, page 166)

AAACorp wants to borrow floatingBBBCorp wants to borrow fixed

Fixed Floating

AAACorp 4.00% 6- month LIBOR 0.1%

BBBCorp 5.20% 6-month LIBOR + 0.6%

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The Swap (Figure 7.6, page 166)

AAACorp BBBCorp

LIBOR

LIBOR+0.6%

4.35%

4%

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The Swap when a Financial

Institution is Involved(Figure 7.7, page 167)

AAA F.I. BBB4%

LIBOR LIBOR

LIBOR+0.6%

4.33% 4.37%

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Criticism of the ComparativeAdvantage Argument

The 4.0% and 5.2% rates available to AAACorpand BBBCorp in fixed rate markets are 5-year ratesThe LIBOR0.1% and LIBOR+0.6% ratesavailable in the floating rate market are six-month rates

BBBCorps fixed rate depends on the spreadabove LIBOR it borrows at in the future

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The Nature of Swap Rates

Six-month LIBOR is a short-term AAborrowing rateThe 5-year swap rate has a riskcorresponding to the situation where 10 six-month loans are made to AA borrowers atLIBOR

This is because the lender can enter into aswap where income from the LIBOR loans isexchanged for the 5-year swap rate

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Using Swap Rates to Bootstrap theLIBOR/Swap Zero Curve

Consider a new swap where the fixed rate is the swaprateWhen principals are added to both sides on the finalpayment date the swap is the exchange of a fixed ratebond for a floating rate bondThe floating-rate rate bond is worth par. The swap isworth zero. The fixed-rate bond must therefore also beworth par

This shows that swap rates define par yield bonds thatcan be used to bootstrap the LIBOR (or LIBOR/swap)zero curve (See Example 7.2 on page 169.)

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Valuation of an Interest RateSwap

Interest rate swaps can be valued asthe difference between the value of afixed-rate bond and the value of afloating-rate bond

Alternatively, they can be valued as a

portfolio of forward rate agreements(FRAs)

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Valuation in Terms of Bonds

The fixed rate bond is valued in the usualway

The floating rate bond is valued by notingthat it is worth par immediately after thenext payment date

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Value of Floating Rate Bond( L =Principal)


0 t *

ValuationDate

First PmtDate

FloatingPmt = k *

SecondPmt Date Maturity

Date

Value = LValue = L +k *

Value = PVof L +k * at t *

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Example

Pay six-month LIBOR, receive 8% (s.a.compounding) on a principal of $100 millionRemaining life 1.25 yearsLIBOR rates for 3-months, 9-months and 15-months are 10%, 10.5%, and 11% (cont comp)6-month LIBOR on last payment date was

10.2% (s.a. compounding)

Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010 20


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Valuation using Bonds (page 172)

Swap value = 98.238 102.505= 4.267

Time Fixed Floating Disc PV fixed PV floatingBond Bond Factor Bond Bond

0.25 4 105.1 0.9753 3.901 102.50450.75 4 0.9243 3.6971.25 104 0.8715 90.64

98.238 102.505

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Valuation in Terms of FRAs

Each exchange of payments in an interest

rate swap is an FRAThe FRAs can be valued on theassumption that todays forward rates are

realized

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Example (page 173)

Time Fixed Floating Net Disc PV of Net

Cash Flow Cash Flow Cash Flow Factor Cash Flow0.25 4 -5.100 -1.100 0.9753 -1.0730.75 4 -5.522 -1.522 0.9243 -1.4071.25 4 -6.051 -2.051 0.8715 -1.787

-4.267

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An Example of a Currency Swap

An agreement to pay 5% on a sterlingprincipal of 10,000,000 & receive 6%on a US$ principal of $15,000,000every year for 5 years

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Exchange of Principal

In an interest rate swap theprincipal is not exchangedIn a currency swap theprincipal is exchanged at thebeginning and the end of theswap

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The Cash Flows (Table 7.5, page 176)

Year

Dollars Pounds$

------millions------2010 18.00 +10.002011 +1.08 0.52012 +1.08 0.52013 +1.08 0.5

2014 +1.08 0.52015 +19.08 10.5

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Typical Uses of aCurrency Swap

Conversion from a liability in one currencyto a liability in another currency

Conversion from an investment in onecurrency to an investment in another

currency

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Comparative Advantage Argumentsfor Currency Swaps (Table 7.6, page 176)

General Electric wants to borrow AUDQantas wants to borrow USD

USD AUD

General Motors 5.0% 7.6%

Qantas 7.0% 8.0%

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Valuation of Currency Swaps

Like interest rate swaps,currency swaps can be valuedeither as the difference between2 bonds or as a portfolio of forward contracts (SeeExamples 7.6 and 7.7)

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Example (pages 178-180)

All Japanese LIBOR/swap rates are 4% All USD LIBOR/swap rates are 9%5% is received in yen; 8% is paid in dollars.Payments are made annuallyPrincipals are $10 million and 1,200 million yenSwap will last for 3 more yearsCurrent exchange rate is 110 yen per dollar

Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010 30


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Valuation in Terms of Bonds

Time Cash Flows ($) PV ($) Cash flows (yen) PV (yen)

1 0.8 0.7311 60 57.65

2 0.8 0.6682 60 55.393 0.8 0.6107 60 53.22

3 10.0 7.6338 1,200 1,064.30

Total 9.6439 1,230.55


Value = 1230.55/1109.6439 = 1.5430

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Valuation in Terms of Forwards


Time $ cashflow

Yen cashflow

ForwardExch rate

Yen cashflow in $

NetCash

Flow

Presentvalue

1 -0.8 60 0.009557 0.5734 -0.2266 -0.2071

2 -0.8 60 0.010047 0.6028 -0.1972 -0.1647

3 -0.8 60 0.010562 0.6337 -0.1663 -0.1269

3 -10.0 1200 0.010562 12.6746 +2.6746 2.0417

Total 1.5430

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Swaps & Forwards

A swap can be regarded as aconvenient way of packaging forwardcontractsWhen a swap is initiated the swap haszero value, but typically some forwardshave a positive value and some have anegative value

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Credit Risk

A swap is worth zero to a companyinitially

At a future time its value is liable to beeither positive or negativeThe company has credit risk exposure

only when its value is positive

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Other Types of Swaps

Amortizing/ step upCompounding swap

Constant maturity swapLIBOR-in-arrears swap

Accrual swap

Equity swap

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O ti F t d Oth D i ti 7th Ed Ch 7 C ight J h C H ll 2010

Other Types of Swaps continued

Cross currency interest rate swapFloating-for-floating currency swap

Diff swapCommodity swapVariance swap

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