paul wilmott on quantitative finance swaps

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1、CHAPTER14swapsInthisChapter...•thespecificationsofbasicinterestrateswapcontracts•therelationshipbetweenswapsandzero-couponbonds•exoticswaps14.1INTRODUCTIONAswapisanagreementbetweentwopartiestoexchange,orswap,futurecashflows.Thesizeofthesecashflowsisdeterminedbysomeformulae,decideduponatthein

2、itiationofthecontract.Theswapsmaybeinasinglecurrencyorinvolvetheexchangeofcashflowsindifferentcurrencies.Theswapsmarketisbig.Thetotalnotionalprincipalamountis,inUSdollars,currentlycomfortablyin14figures.Thismarketreallybeganin1981althoughtherewereasmallnumberofswap-likestructuresarrangedint

3、he1970s.Initiallythemostpopularcontractswerecurrencyswaps,discussedbelow,butveryquicklytheywereovertakenbytheinterestrateswap.14.2THEVANILLAINTERESTRATESWAPIntheinterestrateswapthetwopartiesexchangecashflowsthatarerepresentedbytheinterestonanotionalprincipal.Typ-ically,onesideagreestopayth

4、eotherafixedinterestrateandthecashflowintheoppositedirectionisafloatingrate.ThepartiestoaswapareshownschematicallyinFigure14.1.OneofthecommonestfloatingratesusedinaswapagreementisLIBOR,LondonInterbankOfferRate.Commonlyinaswap,theexchangeofthefixedandfloatinginterestpaymentsoccureverysixmonths.I

5、nthiscasetherelevantLIBORratewouldbethesix-monthrate.Atthematurityofthecontracttheprincipalisnotexchanged.Letmegiveanexampleofhowsuchacontractworks.252PartOnemathematicalandfinancialfoundationsfixedrateApaysBpaysfixedandfloatingandreceivesreceivesfloatingfixedLIBORFigure14.1Thepartiestoani

6、nterestrateswap.ExampleSupposethatweenterintoafive-yearswapon4thAugust2006,withsemi-annualinterestpayments.Wewillpaytotheotherpartyarateofinterestfixedat6%onanotionalprincipalof$100million;thecounterpartywillpayussix-monthLIBOR.ThecashflowsinthiscontractareshowninFigure14.2.Thestraightlinesd

7、enoteafixedrateofinterestandthusaknownamount;thecurlylinesarefloatingratepayments.Thefirstexchangeofpaymentsismadeon4thFebruary2007,sixmonthsafterthedealissigned.Howmuchmoneychangeshandsonthatfirstdate?Wemustpay0.03×$100,000,000=$3,000,000.Thecashflowintheoppositedirecti