1、Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010SwapsChapter 71Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Nature of SwapsA swap is an agreement to exchange cash flows at specified future times according to certain specified rul

2、es2Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010An 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 il

3、lustrates cash flows3Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Millions of DollarsLIBORFLOATING FIXED NetDateRateCash FlowCash FlowCash FlowMar.5, 20104.2%Sept. 5, 20104.8%+2.102.500.40Mar.5, 20115.3%+2.402.500.10Sept. 5, 20115.5%+2.652.50+0.15Mar.5, 20125.6%+

4、2.752.50+0.25Sept. 5, 20125.9%+2.802.50+0.30Mar.5, 20136.4%+2.952.50+0.45Cash Flows to Microsoft(See Table 7.1, page 1594Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Typical Uses of anInterest Rate SwapConverting a liability fromfixed rate to floating rate floati

5、ng rate to fixed rate Converting an investment from fixed rate to floating ratefloating rate to fixed rate 5Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Intel and Microsoft (MS) Transform a Liability(Figure 7.2, page 160)IntelMSLIBOR5%LIBOR+0.1%5.2%6Options, Futu

6、res, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Financial Institution is Involved(Figure 7.4, page 162) F.I.LIBORLIBORLIBOR+0.1%4.985%5.015%5.2%IntelMS7Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Intel and Microsoft (MS) Transform an Asset(F

7、igure 7.3, page 161) IntelMSLIBOR5%LIBOR-0.2%4.7%8Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Financial Institution is Involved(See Figure 7.5, page 163) IntelF.I.MSLIBORLIBOR4.7%5.015%4.985%LIBOR-0.2%9Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyr

8、ight John C. Hull 2010Quotes By a Swap Market Maker (Table 7.3, page 163)MaturityBid (%)Offer (%)Swap Rate (%)2 years6.036.066.0453 years6.216.246.2254 years6.356.396.3705 years 6.476.516.4907 years6.656.686.66510 years6.836.876.85010Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright J

9、ohn C. Hull 2010The Comparative Advantage Argument (Table 7.4, page 166)AAACorp wants to borrow floatingBBBCorp wants to borrow fixedFixed Floating AAACorp4.00%6-month LIBOR 0.1%BBBCorp5.20%6-month LIBOR + 0.6%11Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010The Sw

10、ap (Figure 7.6, page 166) AAACorpBBBCorpLIBORLIBOR+0.6%4.35%4%12Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010The Swap when a Financial Institution is Involved (Figure 7.7, page 167) AAAF.I.BBB4%LIBORLIBORLIBOR+0.6%4.33%4.37%13Options, Futures, and Other Derivativ

11、es, 7th Ed, Ch 7, Copyright John C. Hull 2010Criticism of the Comparative Advantage ArgumentThe 4.0% and 5.2% rates available to AAACorp 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 d

12、epends on the spread above LIBOR it borrows at in the future14Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010The 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

13、loans are made to AA borrowers at LIBORThis is because the lender can enter into a swap where e from the LIBOR loans is exchanged for the 5-year swap rate15Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Using Swap Rates to Bootstrap the LIBOR/Swap Zero CurveConside

14、r a new swap where the fixed rate is the swap rateWhen 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 bondThe floating-rate rate bond is worth par. The swap is worth zero. The fixed-rate bond must therefore also be worth

15、 par This shows that swap rates define par yield bonds that can be used to bootstrap the LIBOR (or LIBOR/swap) zero curve (See Example 7.2 on page 169.)16Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Valuation of an Interest Rate SwapInterest rate swaps can be val

16、ued as the difference between the value of a fixed-rate bond and the value of a floating-rate bondAlternatively, they can be valued as a portfolio of forward rate agreements (FRAs)17Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Valuation in Terms of BondsThe fixed

17、 rate bond is valued in the usual wayThe floating rate bond is valued by noting that it is worth par immediately after the next payment date18Value of Floating Rate Bond (L=Principal)Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 20100t*Valuation DateFirst PmtDateFloat

18、ing Pmt =k*SecondPmt DateMaturity DateValue = LValue = L+k*Value = PV of L+k* at t*19ExamplePay 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 l

19、ast payment date was 10.2% (s.a. compounding)Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 201020Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Valuation using Bonds (page 172) Swap value = 98.238 102.505= 4.26721Options, Futures, an

20、d Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Valuation in Terms of FRAsEach exchange of payments in an interest rate swap is an FRAThe FRAs can be valued on the assumption that todays forward rates are realized22Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C

21、. Hull 2010Example (page 173)23Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010An Example of a Currency Swap An agreement to pay 5% on a sterling principal of 10,000,000 & receive 6% on a US$ principal of $15,000,000 every year for 5 years24Options, Futures, and Oth

22、er Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Exchange of PrincipalIn an interest rate swap the principal is not exchangedIn a currency swap the principal is exchanged at the beginning and the end of the swap25Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2

23、010The Cash Flows (Table 7.5, page 176)YearDollarsPounds$millions2010 18.00 +10.002011 +1.08 0.5 2012 +1.08 0.5 2013 +1.08 0.52014 +1.08 0.5 2015+19.08 10.5 26Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Typical Uses of a Currency SwapConversion from a liability

24、in one currency to a liability in another currencyConversion from an investment in one currency to an investment in another currency27Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Comparative Advantage Arguments for Currency Swaps (Table 7.6, page 176)General Elec

25、tric wants to borrow AUDQantas wants to borrow USDUSDAUDGeneral Motors 5.0%7.6%Qantas 7.0%8.0%28Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Valuation of Currency SwapsLike interest rate swaps, currency swaps can be valued either as the difference between 2 bonds

26、 or as a portfolio of forward contracts (See Examples 7.6 and 7.7)29Example (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 m

27、ore yearsCurrent exchange rate is 110 yen per dollarOptions, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 201030Valuation in Terms of BondsTimeCash Flows ($)PV ($)Cash flows (yen)PV (yen)10.80.73116057.6520.80.66826055.3930.80.61076053.22310.07.63381,2001,064.30Total9.64391,2

28、30.55Options, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Value = 1230.55/1109.6439 = 1.543031Valuation in Terms of ForwardsOptions, Futures, and Other Derivatives, 7th Ed, Ch 7, Copyright John C. Hull 2010Time$ cash flowYen cash flowForward Exch rate Yen cash flow in $Net Cash FlowPresent value1-0.8600.0095570.5734-0.2266-0.20712-0.8600.0100470.6028-0.1972-0.16473-0.8600.0105620.6337-0.1663-0.12693-10.012000.01056212.6746+2.67462.0417Total1.543032Options, Futures, and Other Derivatives, 7th