期货期权及其衍生品配套课件(全34章)Ch07

1、SwapsChapter 7Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20081Nature of SwapsA swap is an agreement to exchange cash flows at specified future times according to certain specified rulesOptions, Futures, and Other Derivatives, 7th International Edition,

2、 Copyright John C. Hull 20082An Example of a “Plain Vanilla” Interest Rate SwapAn 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 millionNext slide illustrates cash flows that could occurOptions, Future

3、s, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20083Cash Flows to Microsoft(See Table 7.1, page 149)Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20084-Millions of Dollars-LIBORFLOATING FIXED NetDateRateCash Flow Cash Flow Cas

4、h FlowMar.5, 20044.2%Sept. 5, 20044.8%+2.102.500.40Mar.5, 20055.3%+2.402.500.10Sept. 5, 20055.5%+2.652.50+0.15Mar.5, 20065.6%+2.752.50+0.25Sept. 5, 20065.9%+2.802.50+0.30Mar.5, 20076.4%+2.952.50+0.45Typical Uses of anInterest Rate SwapConverting a liability fromfixed rate to floating rate floating r

5、ate to fixed rate Converting an investment from fixed rate to floating ratefloating rate to fixed rate Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20085Intel and Microsoft (MS) Transform a Liability(Figure 7.2, page 150)Options, Futures, and Other Deriv

6、atives, 7th International Edition, Copyright John C. Hull 20086IntelMSLIBOR5%LIBOR+0.1%5.2%Financial Institution is Involved(Figure 7.4, page 151) Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20087F.I.LIBORLIBORLIBOR+0.1%4.985%5.015%5.2%IntelMSFinancial

7、Institution has two offsetting swapsIntel and Microsoft (MS) Transform an Asset (Figure 7.3, page 151) Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20088IntelMSLIBOR5%LIBOR-0.2%4.7%Financial Institution is Involved(See Figure 7.5, page 152) Options, Futu

8、res, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20089IntelF.I.MSLIBORLIBOR4.7%5.015%4.985%LIBOR-0.2%Quotes By a Swap Market Maker (Table 7.3, page 153)MaturityBid (%)Offer (%)Swap Rate (%)2 years6.036.066.0453 years6.216.246.2254 years6.356.396.3705 years 6.476.516.4907

9、 years6.656.686.66510 years6.836.876.850Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200810The Comparative Advantage Argument (Table 7.4, page 155) AAACorp wants to borrow floating BBBCorp wants to borrow fixedOptions, Futures, and Other Derivatives, 7th

10、 International Edition, Copyright John C. Hull 200811Fixed Floating AAACorp4.0%6-month LIBOR 0.10%BBBCorp5.2%6-month LIBOR + 0.6%The Swap (Figure 7.6, page 156) Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200812AAACorpBBBCorpLIBORLIBOR+0.6%4.35%4%The Sw

11、ap when a Financial Institution is Involved (Figure 7.7, page 156)Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200813AAACorpF.I.BBBCorp4%LIBORLIBORLIBOR+0.6%4.33%4.37%Criticism of the Comparative Advantage ArgumentThe 4.0% and 5.2% rates available to AAA

12、Corp and BBBCorp in fixed rate markets are 5-year ratesThe LIBOR0.1% and LIBOR+0.6% rates available in the floating rate market are six-month ratesBBBCorps fixed rate depends on the spread above LIBOR it borrows at in the futureOptions, Futures, and Other Derivatives, 7th International Edition, Copy

13、right John C. Hull 200814The Nature of Swap RatesSix-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 LIBORThis is because the lender can enter into a swap where income from the LIBOR loa

14、ns is exchanged for the 5-year swap rateOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200815Using Swap Rates to Bootstrap the LIBOR/Swap Zero CurveConsider a new swap where the fixed rate is the swap rateWhen principals are added to both sides on the fina

15、l payment date the swap is the exchange of a fixed rate bond for a floating rate bondThe 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 LI

16、BOR/swap) zero curveOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200816Valuation of an Interest Rate Swap That Is Not NewInterest rate swaps can be valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bondAlter

17、natively, they can be valued as a portfolio of forward rate agreements (FRAs)Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200817Valuation in Terms of BondsThe fixed rate bond is valued in the usual wayThe floating rate bond is valued by noting that it is

18、 worth par immediately after the next payment dateOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200818ExamplePay 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 1

19、5-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 International Edition, Copyright John C. Hull 200819Valuation Using Bonds (page 160) Options, Futures, and Other Derivatives, 7th International Edit

20、ion, Copyright John C. Hull 200820TimeBfix cash flowBfl cash flowDisc factorPV BfixPV Bfl0.254.0105.1000.97533.901102.5050.754.00.92433.6971.25104.00.871590.640Total98.238102.505Valuation in Terms of FRAsEach exchange of payments in an interest rate swap is an FRAThe FRAs can be valued on the assump

21、tion that todays forward rates are realizedOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200821Valuation of Example Using FRAs (page 162)TimeFixed cash flowFloating cash flowNet Cash FlowDisc factorPV Bfl0.254.0-5.100-1.1000.9753-1.0730.754.0-5.522-1.5220

22、.9243-1.4071.254.0-6.051-2.0510.8715-1.787Total-4.267Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200822An Example of a Currency SwapAn agreement to pay 5% on a sterling principal of 10,000,000 & receive 6% on a US$ principal of $18,000,000 every yea

23、r for 5 yearsOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200823Exchange of PrincipalIn an interest rate swap the principal is not exchangedIn a currency swap the principal is usually exchanged at the beginning and the end of the swaps lifeOptions, Futur

24、es, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200824The Cash Flows (Table 7.7, page 164)Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200825YearDollarsPounds$-millions-2004 18.00 +10.002005 +1.08 0.50 2006 +1.08 0.50 2007 +1

25、.08 0.502008 +1.08 0.50 2009+19.08 10.50 Typical Uses of a Currency SwapConversion from a liability in one currency to a liability in another currencyConversion from an investment in one currency to an investment in another currencyOptions, Futures, and Other Derivatives, 7th International Edition,

26、Copyright John C. Hull 200826Comparative Advantage Arguments for Currency Swaps (Table 7.8, page 165)General Electric wants to borrow AUDQantas wants to borrow USDOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200827USDAUDGeneral Motors 5.0%7.6%Qantas 7.0%

27、8.0%Valuation of Currency SwapsLike interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contractsOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200828ExampleAll Japanese LIBOR/swap rates a

28、re 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 dollarOptions, Futures, and Other Derivatives, 7th International Edition, Co

29、pyright John C. Hull 200829Valuation in Terms of Bonds (Table 7.9, page 167)TimeCash Flows ($) PV ($)Cash flows (yen) PV (yen)10.80.73116057.6520.80.66826055.3930.80.61076053.22310.07.63381,2001,064.30Total9.64391,230.55Options, Futures, and Other Derivatives, 7th International Edition, Copyright Jo

30、hn C. Hull 200830Valuation in Terms of Forwards (Table 7.10, page 168)Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200831Time$ cash flowYen cash flowForward Exch rate Yen cash flow in $Net Cash FlowPresent value1-0.8600.0095570.5734-0.2266-0.20712-0.8600

31、.0100470.6028-0.1972-0.16473-0.8600.0105620.6337-0.1663-0.12693-10.012000.01056212.6746+2.67462.0417Total1.5430Swaps & ForwardsA swap can be regarded as a convenient way of packaging forward contractsAlthough the swap contract is usually worth zero at the outset, each of the underlying forward contracts are not wor