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1、FinancialCalculusSong-PingZhuSchoolofMathematicsandAppliedStatisticsUniversityofWollongongWollongongNSW2522AUSTRALIAChapter1IntroductionAderivativesecurityisasecuritywhosevaluedependsonthevalueofothermorebasicunderlyingvariables.e.g.,•Forwardcontracts
2、,•Futurecontracts,•Options,•Swaps,•Convertiblebonds,etc.Derivativesecuritiesarealsocalledcontingentclaims,1derivativeproducts,orjustsimplyderivatives.Inthiscourse,weshallfocusonthevaluationoffuturesandoptions.§1.1ForwardandFuturesContractsAforwardcont
3、ractisanagreementtobuyorsellanasset(called“underlyingasset”)atacertainfuturetimeforacertainfutureprice(knownasforwardprice).Thedeliveryprice:Thespecifiedpriceinaforwardcontractisreferredtoasthedeliverypriceandthespecifieddateinthefutureiscalledthedeli
4、verydateormaturitydate.Forwardcontractsarenormallynottradedonan2exchange.Longposition:Thepartywhoagreestobuytheunderlyingassetissaidtoholdalongposition.Shortposition:Thepartywhoagreestoselltheunderlyingassetissaidtoholdashortposition.Example1.1Table1s
5、howsthespotandforwardforeignexchangequoteson26/2/07US$/A$Spot0.792130-dayforward0.795490-dayforward0.8021180-dayforward0.8327Here,thespotrateisthecurrentexchangeratebetween3A$andUS$.Ifyouhaveagreedona30-daycontracttobuyUS$in30days,youhaveenteredintoal
6、ongposition.Thedeliverydateis30daysfromtodayandthedeliveryprice(thepurchaseprice)isA$1US$0.7954.Similarly,youmaywriteaforwardcontracttobuyorsell$USin90days,or180days.Question:Howisthedeliverypricedetermined?Atthetimethecontractisenteredinto,thedelive
7、rypriceischosensothatthevalueoftheforwardcontracttobothpartiesiszero.Therefore,neitherpartyhastopayanythingtoenterintoaforwardcontract.4TheForwardPrice:Theforwardpriceforaforwardcontractisdefinedbythedeliverypricewhenenteringanewcontracttodaybasedonto
8、day'sunderlyingassetvalue.Inotherwords,thisisthedeliverypriceatthetimewhenaforwardcontractisinitiated.So,ifweuseKtodenotethedeliverypriceandFtheforwardprice,F=Katt=0,wheretisthecurrenttime.OnceanF.C.(forwardcontractfromnowon)isenteredinto,Kisf
