Heston-original.pdf

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1、AClosed-FormSolutionforOptionswithStochasticVolatilitywithApplicationstoBondandCurrencyOptionsStevenL.HestonYaleUniversityIuseanewtechniquetoderiveaclosed-formsolu-tionforthepriceofaEuropeancalloptiononanassetwithstochasticvolatility.Themodelallowsarbitraryc

2、orrelationbetweenvolatilityandspot-assetreturns.Iintroducestochasticinterestratesandshowhowtoapplythemodeltobondoptionsandforeigncurrencyoptions.Simulationsshowthatcorrelationbetweenvolatilityandthespotassetspriceisimportantforexplainingreturnskewnessandstri

3、ke-pricebiasesintheBlack-Scholes(1973)model.Thesolutiontechniqueisbasedoncharacteristicfunctionsandcanbeappliedtootherproblems.ManyplauditshavebeenaptlyusedtodescribeBlackandScholes(1973)contributiontooptionpricingtheory.Despitesubsequentdevelopmentofoptiont

4、heory,theoriginalBlack-ScholesformulaforaEuro-peancalloptionremainsthemostsuccessfulandwidelyusedapplication.ThisformulaisparticularlyusefulbecauseitrelatesthedistributionofspotreturnsIthankHansKnochforcomputationalassistance.IamgratefulforthesuggestionsofHy

5、engKeun(thereferee)andforcommentsbyparticipantsata1992NationalBureauofEconomicResearchseminarandtheQueensUniversity1992DerivativeSecuritiesSymposium.Anyremainingerrorsaremyresponsibility.AddresscorrespondencetoStevenL.Heston,YaleSchoolofOrganizationandManage

6、ment,135ProspectStreet,NewHaven,CT06511.TheReviewofFinancialStudies1993Volume6,number2,pp.327-343©1993TheReviewofFinancialStudies0893-9454/93/$1.50TheReviewofFinancialStudies/v6n21993tothecross-sectionalpropertiesofoptionprices.Inthisarticle,Igeneralizethemo

7、delwhileretainingthisfeature.AlthoughtheBlack–Scholesformulaisoftenquitesuccessfulinexplainingstockoptionprices[BlackandScholes(1972)],itdoeshaveknownbiases[Rubinstein(1985)].Itsperformancealsoissub-stantiallyworseonforeigncurrencyoptions[MelinoandTurnbull(1

8、990,1991),Knoch(1992)].Thisisnotsurprising,sincetheBlack-Scholesmodelmakesthestrongassumptionthat(continuouslycom-pounded)stockreturnsarenormallydistributedwithknownmeanandvariance.SincetheBlack