衍生工具与风险管理第3章课件

D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:1Chapter3:PrinciplesofOptionPricingAskingafundmanageraboutarbitrageopportunitiesisakintoaskingafishermanwherehisfavoriteholeis.Hewillbegladtotellyouafishstoryfromlongago,buthewillnottellyouwherehecaughtthetroutthatinouranalogycanbetranslatedintomillionsofdollars,lesttherewillbehundredsoffishermeninhisspotpullingintheirowntroutandreducingtheinefficiencythatmadethatarbitrageopportunityprofitableinthefirstplace.DanielP.CollinsFutures,December,2001,p.66D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:2ImportantConceptsinChapter3RoleofarbitrageinpricingoptionsMinimumvalue,maximumvalue,valueatexpirationandlowerboundofanoptionpriceEffectofexerciseprice,timetoexpiration,risk-freerateandvolatilityonanoptionpriceDifferencebetweenpricesofEuropeanandAmericanoptionsPut-callparityD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:3BasicNotationandTerminologySymbolsS0(stockprice)X(exerciseprice)T(timetoexpiration=(daysuntilexpiration)/365)r(seebelow)ST(stockpriceatexpiration)C(S0,T,X),P(S0,T,X)D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:4BasicNotationandTerminology(continued)Computationofrisk-freerateDate:May14.Optionexpiration:May21T-billbiddiscount=4.45,askdiscount=4.37AverageT-billdiscount=(4.45+4.37)/2=4.41T-billprice=100-4.41(7/360)=99.91425T-billyield=(100/99.91425)(365/7)-1=.0457So4.57%isrisk-freerateforoptionsexpiringMay21Otherrisk-freerates:4.56(June18),4.63(July16)SeeTable3.1,p.58forpricesofAOLoptionsD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:5PrinciplesofCallOptionPricingTheMinimumValueofaCallC(S0,T,X)0(foranycall)ForAmericancalls:Ca(S0,T,X)Max(0,S0-X)Conceptofintrinsicvalue:Max(0,S0-X)ProofofintrinsicvalueruleforAOLcallsConceptoftimevalueSeeTable3.2,p.59fortimevaluesofAOLcallsSeeFigure3.1,p.60forminimumvaluesofcallsD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:6PrinciplesofCallOptionPricing(continued)TheMaximumValueofaCallC(S0,T,X)S0IntuitionSeeFigure3.2,p.61,whichaddsthistoFigure3.1TheValueofaCallatExpirationC(ST,0,X)=Max(0,ST-X)Proof/intuitionForAmericanandEuropeanoptionsSeeFigure3.3,p.63D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:7PrinciplesofCallOptionPricing(continued)TheEffectofTimetoExpirationTwoAmericancallsdifferingonlybytimetoexpiration,T1andT2whereT1T2.Ca(S0,T2,X)Ca(S0,T1,X)Proof/intuitionDeepin-andout-of-the-moneyTimevaluemaximizedwhenat-the-moneyConceptoftimevaluedecaySeeFigure3.4,p.64andTable3.2,p.59Cannotbeproven(yet)forEuropeancallsD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:8PrinciplesofCallOptionPricing(continued)TheEffectofExercisePriceTheEffectonOptionValueTwoEuropeancallsdifferingonlybystrikesofX1andX2.Whichisgreater,Ce(S0,T,X1)orCe(S0,T,X2)?ConstructportfoliosAandB.SeeTable3.3,p.65.PortfolioAhasnon-negativepayoff;therefore,•Ce(S0,T,X1)Ce(S0,T,X2)•Intuition:showwhathappensifnottruePricesofAOLoptionsconformD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:9PrinciplesofCallOptionPricing(continued)TheEffectofExercisePrice(continued)LimitsontheDifferenceinPremiumsAgain,noteTable3.3,p.65.Wemusthave•(X2-X1)(1+r)-TCe(S0,T,X1)-Ce(S0,T,X2)•X2-X1Ce(S0,T,X1)-Ce(S0,T,X2)•X2-X1Ca(S0,T,X1)-Ca(S0,T,X2)•ImplicationsSeeTable3.4,p.67.PricesofAOLoptionsconformD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:10PrinciplesofCallOptionPricing(continued)TheLowerBoundofaEuropeanCallConstructportfoliosAandB.SeeTable3.5,p.68.BdominatesA.Thisimpliesthat(afterrearranging)Ce(S0,T,X)Max[0,S0-X(1+r)-T]ThisisthelowerboundforaEuropeancallSeeFigure3.5,p.69forthepricecurveforEuropeancallsDividendadjustment:subtractpresentvalueofdividendsfromS;adjustedstockpriceisS´Forforeigncurrencycalls,Ce(S0,T,X)Max[0,S0(1+)-T-X(1+r)-T]D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:11PrinciplesofCallOptionPricing(continued)AmericanCallVersusEuropeanCallCa(S0,T,X)Ce(S0,T,X)ButS0-X(1+r)-TS0-XpriortoexpirationsoCa(S0,T,X)Max(0,S0-X(1+r)-T)LookatTable3.6,p.70forlowerboundsofAOLcallsIftherearenodividendsonthestock,anAmericancallwillneverbeexercisedearly.Itwillalwaysbebettertosellthecallinthemarket.IntuitionD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:12PrinciplesofCallOptionPricing(continued)TheEarlyExerciseofAmericanCallsonDividend-PayingStocksIfastockpaysadividend,itispossiblethatanAmericancallwillbeexercisedascloseaspossibletotheex-dividenddate.(Foracurrency,theforeigninterestcaninduceearlyexercise.)IntuitionTheEffectofInterestRatesTheEffectofStockVolatilityD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.3:13PrinciplesofPutOptionPricingTheMinimumValueofaPutP(S0,T,X)0(foranyput)ForAmericanputs:Pa(S0,T,X)Max(0,X-S0)Conceptofintrinsicvalue:Max(0,X-S0)ProofofintrinsicvalueruleforAOLputsSeeFigure3.6,p.74forminimumvaluesofputsConceptoftimevalueS