衍生工具与风险管理第4章课件.ppt

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1、Chapter4:OptionPricingModels:TheBinomialModelYoucanthinkofaderivativeasamixtureofitsconstituentunderliersmuchasacakeisamixtureofeggs,flour,andmilkincarefullyspecifiedproportions.Thederivative’smodelprovidesarecipeforthemixture,onewhoseingredients’quantitiesvarywithtime.EmanuelDermanRisk,July,200

2、1,p.48D.M.ChanceCh.4:1AnIntroductiontoDerivativesandRiskManagement,6thed.ImportantConceptsinChapter4TheconceptofanoptionpricingmodelTheone-andtwo-periodbinomialoptionpricingmodelsExplanationoftheestablishmentandmaintenanceofarisk-freehedgeIllustrationofhowearlyexercisecanbecapturedTheextensionoft

3、hebinomialmodeltoanynumberoftimeperiodsAlternativespecificationsofthebinomialmodelDefinitionofamodelAsimplifiedrepresentationofrealitythatusescertaininputstoproduceanoutputorresultDefinitionofanoptionpricingmodelAmathematicalformulathatusesthefactorsthatdetermineanoption’spriceasinputstoproduceth

4、etheoreticalfairvalueofanoption.TheOne-PeriodBinomialModelConditionsandassumptionsOneperiod,twooutcomes(states)S=currentstockpriceu=1+returnifstockgoesupd=1+returnifstockgoesdownr=risk-freerateValueofEuropeancallatexpirationoneperiodlaterCu=Max(0,Su-X)orCd=Max(0,Sd-X)SeeFigure4.1,p.98TheOne-Perio

5、dBinomialModel(continued)Importantpoint:d<1+r

6、el(continued)ThesevaluesareallknownsohiseasilycomputedSincetheportfolioisriskless,itshouldearntherisk-freerate.ThusV(1+r)=Vu(orVd)SubstitutingforVandVu(hS-C)(1+r)=hSu-CuAndthetheoreticalvalueoftheoptionisTheOne-PeriodBinomialModel(continued)Thisisthetheoreticalvalueofthecallasdeterminedbythestock

7、price,exerciseprice,risk-freerate,andupanddownfactors.Theprobabilitiesoftheupanddownmoveswereneverspecified.Theyareirrelevanttotheoptionprice.TheOne-PeriodBinomialModel(continued)AnIllustrativeExampleS=100,X=100,u=1.25