衍生工具与风险管理第4章课件PPT文件格式下载.ppt
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衍生工具与风险管理第4章课件PPT文件格式下载.ppt
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Chapter4:
@#@OptionPricingModels:
@#@TheBinomialModelYouYoucancanthinkthinkofofaaderivativederivativeasasaamixturemixtureofofitsitsconstituentconstituentunderliersunderliersmuchmuchasasaacakecakeisisaamixturemixtureofofeggs,eggs,flour,flour,andandmilkmilkinincarefullycarefullyspecifiedspecifiedproportions.proportions.TheThederivativesderivativesmodelmodelprovidesprovidesaareciperecipeforforthethemixture,mixture,oneonewhosewhoseingredientsquantitiesvarywithtime.ingredientsquantitiesvarywithtime.EmanuelEmanuelDermanDermanRiskRisk,July,2001,p.48,July,2001,p.48D.M.ChanceCh.4:
@#@1AnIntroductiontoDerivativesandRiskManagement,6thed.ImportantConceptsinChapter4nnTheconceptofanoptionpricingmodelTheconceptofanoptionpricingmodelnnTheone-andtwo-periodbinomialoptionpricingmodelsTheone-andtwo-periodbinomialoptionpricingmodelsnnExplanationoftheestablishmentandmaintenanceofaExplanationoftheestablishmentandmaintenanceofarisk-freehedgerisk-freehedgennIllustrationofhowearlyexercisecanbecapturedIllustrationofhowearlyexercisecanbecapturednnTheextensionofthebinomialmodeltoanynumberofTheextensionofthebinomialmodeltoanynumberoftimeperiodstimeperiodsnnAlternativespecificationsofthebinomialmodelAlternativespecificationsofthebinomialmodelD.M.Chance2AnIntroductiontoDerivativesandRiskManagement,6thed.nnDefinitionofamodelDefinitionofamodeluuAAsimplifiedsimplifiedrepresentationrepresentationofofrealityrealitythatthatusesusescertaincertaininputstoproduceanoutputorresultinputstoproduceanoutputorresultnnDefinitionofanoptionpricingmodelDefinitionofanoptionpricingmodeluuAAmathematicalmathematicalformulaformulathatthatusesusesthethefactorsfactorsthatthatdeterminedetermineananoptionsoptionspricepriceasasinputsinputstotoproduceproducethethetheoreticalfairvalueofanoption.theoreticalfairvalueofanoption.D.M.Chance3AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModelnnConditionsandassumptionsConditionsandassumptionsuuOneperiod,twooutcomes(states)Oneperiod,twooutcomes(states)uuS=currentstockpriceS=currentstockpriceuuu=1+returnifstockgoesupu=1+returnifstockgoesupuud=1+returnifstockgoesdownd=1+returnifstockgoesdownuur=risk-freerater=risk-freeratennValueofEuropeancallatexpirationoneperiodlaterValueofEuropeancallatexpirationoneperiodlateruuCCuu=Max(0,Su-X)or=Max(0,Su-X)oruuCCdd=Max(0,=Max(0,SdSd-X)-X)nnSeeSeeFigure4.1,p.98Figure4.1,p.98D.M.Chance4AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModel(continued)nnImportantpoint:
@#@d1+rutopreventarbitrageImportantpoint:
@#@d1+rutopreventarbitragennWeconstructahedgeportfolioofhsharesofstockandoneWeconstructahedgeportfolioofhsharesofstockandoneshortcall.Currentvalueofportfolio:
@#@shortcall.Currentvalueofportfolio:
@#@uuV=V=hShS-C-CnnAtexpirationthehedgeportfoliowillbeworthAtexpirationthehedgeportfoliowillbeworthuuVVuu=hSuhSu-C-CuuuuVVdd=hSdhSd-CCdduuIfwearehedged,thesemustbeequal.SettingVIfwearehedged,thesemustbeequal.SettingVuu=VVddandsolvingforhgivesandsolvingforhgivesD.M.Chance5AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModel(continued)nnThesevaluesareallknownsohiseasilycomputedThesevaluesareallknownsohiseasilycomputednnSincetheportfolioisSincetheportfolioisrisklessriskless,itshouldearntherisk-free,itshouldearntherisk-freerate.Thusrate.ThusuuV(1+r)=VV(1+r)=Vuu(or(orVVdd)nnSubstitutingforVandVSubstitutingforVandVuuuu(hShS-C)(1+r)=-C)(1+r)=hSuhSu-C-CuunnAndthetheoreticalvalueoftheoptionisAndthetheoreticalvalueoftheoptionisD.M.Chance6AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModel(continued)nnThisisthetheoreticalvalueofthecallasdeterminedbyThisisthetheoreticalvalueofthecallasdeterminedbythestockprice,exerciseprice,risk-freerate,andupandthestockprice,exerciseprice,risk-freerate,andupanddownfactors.downfactors.nnTheprobabilitiesoftheupanddownmoveswereneverTheprobabilitiesoftheupanddownmoveswereneverspecified.Theyareirrelevanttotheoptionprice.specified.Theyareirrelevanttotheoptionprice.D.M.Chance7AnIntroductiontoDerivativesandRiskManagement,6thed.TheOne-PeriodBinomialModel(continued)nnAnIllustrativeExampleAnIllustrativeExampleuuS=100,X=100,u=1.25,d=0.80,r=.07S=100,X=100,u=1.25,d=0.80,r=.07uuFirstfindthevaluesofCFirstfindthevaluesofCuu,CCdd,h,andp:
@#@,h,andp:
@#@FFCCuu=Max(0,100(1.25)-100)=Max(0,125-100)=Max(0,100(1.25)-100)=Max(0,125-100)=2525FFCCdd=Max(0,100(.80)-100)=Max(0,80-100)=0=Max(0,100(.80
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- 衍生 工具 风险 管理 课件