Swaps

Chapter 7SwapsOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201411Nature of SwapsA swap is an agreement to exchange cash flows at specified future times according to certain specified rulesOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20142An 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 occur (Day count conventions are not considered)Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20143One Possible Outcome for Cash Flows to Microsoft (Table 7.1, page 155)DateLIBOR Floating Cash FlowFixed Cash FlowNet Cash FlowMar 5, 20144.20%Sep 5, 20144.80%+2.102.500.40Mar 5, 20155.30%+2.402.500.10Sep 5, 20155.50%+2.652.50+ 0.15Mar 5, 20165.60%+2.752.50+0.25Sep 5, 20165.90%+2.802.50+0.30Mar 5, 2017+2.952.50+0.45Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201444Typical Uses of an Interest Rate SwapConverting a liability fromfixed rate to floating rate floating rate to fixed rate

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

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20145Intel and Microsoft (MS) Transform a Liability (Figure 7.2, page 155)

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20146IntelMSLIBOR5%LIBOR+0.1%5.2%Financial Institution is Involved(Figure 7.4, page 157) Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20147F.I.LIBORLIBORLIBOR+0.1%4.985%5.015%5.2%IntelMSFinancial Institution has two offsetting swapsIntel and Microsoft (MS) Transform an Asset (Figure 7.3, page 156)

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20148IntelMSLIBOR5%LIBOR-0.2%4.7%Financial Institution is Involved(See Figure 7.5, page 157) Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20149IntelF.I.MSLIBORLIBOR4.7%5.015%4.985%LIBOR-0.2%Quotes By a Swap Market Maker (Table 7.3, page 158)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 years6.836.876.850Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201410Day CountA day count convention is specified for for fixed and floating paymentFor example, LIBOR is likely to be actual/360 in the US because LIBOR is a money market rate Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20141111ConfirmationsConfirmations specify the terms of a transactionThe International Swaps and Derivatives has developed Master Agreements that can be used to cover all agreements between two counterpartiesMany interest rate swaps are now cleared through a CCP such as LCH Clearnet or the CME GroupOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20141212The Comparative Advantage Argument (Table 7.4, page 160)AAACorp wants to borrow floatingBBBCorp wants to borrow fixedOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201413FixedFloatingAAACorp4.0%6 month LIBOR 0.1%BBBCorp5.2%6 month LIBOR + 0.6%The Swap (Figure 7.6, page 161) Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201414AAACorpBBBCorpLIBORLIBOR+0.6%4.35%4%The Swap when a Financial Institution is Involved (Figure 7.7, page 162) Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201415AAACorpF.I.BBBCorp4%LIBORLIBORLIBOR+0.6%4.33%4.37%Criticism 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 depends on the spread above LIBOR it borrows at in the futureOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201416The 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 loans is exchanged for the 5-year swap rateOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201417The Discount RatePre-crisis derivatives cash flows were discounted at LIBORAs Chapter 9 explains, this has changedHere we illustrate the valuation methodology by assuming that LIBOR is the discount rate

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201418Using 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 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 assuming LIBOR discounting is used. 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 curveOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201419Example of Bootstrapping the LIBOR/Swap Curve (Example 7.1, page 164)6-month, 12-month, and 18-month LIBOR/swap rates are 4%, 4.5%, and 4.8% with continuous compounding.Two-year swap rate is 5% (semiannual)

The 2-year LIBOR/swap rate, R, is 4.953%

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201420

20Valuation of an Interest Rate SwapInitially interest rate swaps are worth close to zeroAt later times they can be valued 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)Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201421Valuation in Terms of BondsThe fixed 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 dateOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201422Valution of Floating-Rate BondOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 2014230t*Valuation DateFirst PmtDateFloating Pmt =k*SecondPmt DateMaturity DateValue = LValue = L+k*Value = PV of L+k* at t*23ExampleReceive six-month LIBOR, pay 3% (s.a. compounding) on a principal of $100 millionRemaining life 1.25 yearsLIBOR zero rates for 3-months, 9-months and 15-months are 2.8%, 3%, and 3.2% (cont comp)6-month LIBOR on last payment date was 12.9% (s.a. compounding)Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20142424Valuation Using Bonds (page 166) Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201425TimeBfix cash flowBfl cash flowDisc factorPV BfixPV Bfl0.251.5101.4500.99301.4895100.74230.751.50.97631.46441.25101.50.958497.2766Total100.2306100.7423Swap value = 100.7423 100.2306 = 0.511725Valuation in Terms of FRAsEach exchange of payments in an interest rate swap is an FRAThe FRAs can be valued on the assumption that todays forward rates are realizedOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201426Valuation of Example Using FRAs (page 167)TimeFixed cash flowFloating cash flowNet Cash FlowDisc factorPV Bfl0.251.5000+1.45000.00500.99300.04970.751.5000+1.7145+0.21450.9763+0.20941.251.5000+1.8672+0.36720.9584+0.3519Total+0.5117Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 20142727An Example of a Currency SwapAn agreement to pay 5% on a sterling principal of 10,000,000 & receive 6% on a US$ principal of $15,000,000 every year for 5 yearsOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201428Exchange 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, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201429The Cash Flows (Table 7.7, page 170)Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201430DateDollar Cash Flows(millions)Sterling cash flow(millions)Feb 1, 201415.00+10.0Feb 1, 2015 +0.90 0.50Feb 1, 2016 +0.90 0.50Feb 1, 2017 +0.90 0.50Feb 1, 2018 +0.90 0.50Feb 1, 2019+15.9010.50

Typical Uses of a Currency SwapConvert a liability in one currency to a liability in another currencyConvert an investment in one currency to an investment in another currency

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201431Comparative Advantage May Be Real Because of Taxes General Electric wants to borrow AUD Quantas wants to borrow USD Costs after adjusting for the differential impact of taxes:Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201432USDAUDGeneral Electric5.0%7.6%Quantas7.0%8.0%32Valuation 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, 9th Edition, Copyright John C. Hull 201433ExampleAll 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, 9th Edition, Copyright John C. Hull 20143434Valuation in Terms of Bonds (Table 7.9, page 173)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, 9th Edition, Copyright John C. Hull 201435Value of Swap = 1230.55/110 9.6439 = 1.5430 35Valuation in Terms of Forwards (Table 7.10, page 174)Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201436Time$ 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+2.67462.0417Total1.543036Swaps & ForwardsA swap can be regarded as a convenient way of packaging forward contractsAlthough the swap contract is usually worth close to zero at the outset, each of the underlying forward contracts are not worth zeroOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201437Credit Risk: Single Uncollateralized Transaction with CounterpartyA swap is worth zero to a company initiallyAt a future time its value is liable to be either positive or negativeThe company has credit risk exposure only when ithe value is positiveSome swaps are more likely to lead to credit risk exposure than othersWhat is the situation if early forward rates have a positive value?What is the situation when the early forward rates have a negative value?

Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201438Other Types of SwapsFloating-for-floating interest rate swapsamortizing swapsstep up swapsforward swapsconstant maturity swapscompounding swapsLIBOR-in-arrears swapsaccrual swapsdiff swapscross currency interest rate swapsequity swapsextendable swapsputtable swapsswaptionscommodity swapsvolatility swapsetc etcOptions, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull 201439