衍生工具与风险管理全套配套课件DonM.Chance ch04.ppt

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1、Chapter4:OptionPricingModels:TheBinomialModelYoucanthinkofaderivativeasamixtureofitsconstituentunderliersmuchasacakeisamixtureofeggs,flour,andmilkincarefullyspecifiedproportions.Thederivative’smodelprovidesarecipeforthemixture,onewhoseingredients’quantitiesvarywithtime.EmanuelDe

2、rmanRisk,July,2001,p.48D.M.ChanceCh.4:1AnIntroductiontoDerivativesandRiskManagement,6thed.ImportantConceptsinChapter4TheconceptofanoptionpricingmodelTheone-andtwo-periodbinomialoptionpricingmodelsExplanationoftheestablishmentandmaintenanceofarisk-freehedgeIllustrationofhowearlyex

3、ercisecanbecapturedTheextensionofthebinomialmodeltoanynumberoftimeperiodsAlternativespecificationsofthebinomialmodelD.M.Chance2AnIntroductiontoDerivativesandRiskManagement,6thed.DefinitionofamodelAsimplifiedrepresentationofrealitythatusescertaininputstoproduceanoutputorresultDefi

4、nitionofanoptionpricingmodelAmathematicalformulathatusesthefactorsthatdetermineanoption’spriceasinputstoproducethetheoreticalfairvalueofanoption.D.M.Chance3AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModelConditionsandassumptionsOneperiod,twooutcomes(s

5、tates)S=currentstockpriceu=1+returnifstockgoesupd=1+returnifstockgoesdownr=risk-freerateValueofEuropeancallatexpirationoneperiodlaterCu=Max(0,Su-X)orCd=Max(0,Sd-X)SeeFigure4.1,p.98D.M.Chance4AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModel(continued)I

6、mportantpoint:d<1+r

7、tivesandRiskManagement,6thed.TheOne-PeriodBinomialModel(continued)ThesevaluesareallknownsohiseasilycomputedSincetheportfolioisriskless,itshouldearntherisk-freerate.ThusV(1+r)=Vu(orVd)SubstitutingforVandVu(hS-C)(1+r)=hSu-CuAndthetheoreticalvalueoftheoptionisD.M.Chance6AnIntroducti

8、ontoDerivativesandRiskManagement,6thed.T