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1、JournalofFinancialEconomics7(1979)229-263.0North-HollandPublishingCompanyOPTIONPRICING:ASIMPLIFIEDAPPROACH*JohnC.COXMassachusettsInstituteofTechnology,Cambridge,MA02139,USAStanfordUniversity,Stanford,CA94305,USAStephenA.ROSSYaleUniversity,NewHaven,CT06520,USAMarkRUBINSTEINUniversityofCaliforma,
2、Berkeley,CA94720,USAReceivedMarch1979,revisedversionreceivedJuly1979Thispaperpresentsasimplediscrete-timemodelforvalumgoptlons.ThefundamentalecononucprinciplesofoptionpricingbyarbitragemethodsareparticularlyclearInthissetting.Itsdevelopmentrequiresonlyelementarymathematics,yetitcontainsasaspeci
3、allimitingcasethecelebratedBlack-&holesmodel,whichhaspreviouslybeenderivedonlybymuchmoredifficultmethods.Thebasicmodelreadilylendsitselftogeneralizationinmanyways.Moreover,byitsveryconstructlon,itgivesrisetoasimpleandefficientnumericalprocedureforvalumgoptlonsforwhichprematureexercisemaybeoptim
4、al.1.IntroductionAnoptionisasecuritywhichgivesitsownertherighttotradeinafixednumberofsharesofaspecifiedcommonstockatafixedpriceatanytimeonorbeforeagivendate.Theactofmakingthistransactionisreferredtoasexercisingtheoption.Thefixedpriceistermedthestrikingprice,andthegivendate,theexpirationdate.Aca
5、lloptiongivestherighttobuytheshares;aputoptiongivestherighttoselltheshares.Optionshavebeentradedforcenturies,buttheyremainedrelativelvobscurefinancialinstrumentsuntiltheintroductionofalistedoptionsexchangein1973.Sincethen,optionstradinghasenjoyedanexpansionunprecedentedinAmericansecuritiesmarke
6、ts.Optionpricingtheoryhasalongandillustrioushistory,butitalsounderwentarevolutionarychangein1973.Atthattime,FischerBlackand*OurbestthanksgotoWilliamSharpe,whofirstsuggestedtoustheadvantagesofthediscrete-timeapproachtooptionprlcmgdevelopedhere.Wearealsogratefultoourstudentsoverthepastseveralyear
7、s.Thenfavorablereactlonstothiswayofpresentingthingsencouragedustowritethisarticle.WehavereceivedsupportfromtheNationalScienceFoundationunderGrantsNos.SOC-77-18087andSOC-77-22301.230J.C.Coxetal.,Optwnprrcrng.Arrn~plr/wd~~ppnw~IrMyr
