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1、Chapter3:PrinciplesofOptionPricingAskingafundmanageraboutarbitrageopportunitiesisakintoaskingafishermanwherehisfavoriteholeis.Hewillbegladtotellyouafishstoryfromlongago,buthewillnottellyouwherehecaughtthetroutthatinouranalogycanbetranslatedintomillionsof
2、dollars,lesttherewillbehundredsoffishermeninhisspotpullingintheirowntroutandreducingtheinefficiencythatmadethatarbitrageopportunityprofitableinthefirstplace.DanielP.CollinsFutures,December,2001,p.66D.M.ChanceCh.3:1AnIntroductiontoDerivativesandRiskManage
3、ment,6thed.ImportantConceptsinChapter3RoleofarbitrageinpricingoptionsMinimumvalue,maximumvalue,valueatexpirationandlowerboundofanoptionpriceEffectofexerciseprice,timetoexpiration,risk-freerateandvolatilityonanoptionpriceDifferencebetweenpricesofEuropeana
4、ndAmericanoptionsPut-callparityD.M.Chance2AnIntroductiontoDerivativesandRiskManagement,6thed.BasicNotationandTerminologySymbolsS0(stockprice)X(exerciseprice)T(timetoexpiration=(daysuntilexpiration)/365)r(seebelow)ST(stockpriceatexpiration)C(S0,T,X),P(S0,
5、T,X)D.M.Chance3AnIntroductiontoDerivativesandRiskManagement,6thed.BasicNotationandTerminology(continued)Computationofrisk-freerateDate:May14.Optionexpiration:May21T-billbiddiscount=4.45,askdiscount=4.37AverageT-billdiscount=(4.45+4.37)/2=4.41T-billprice=
6、100-4.41(7/360)=99.91425T-billyield=(100/99.91425)(365/7)-1=.0457So4.57%isrisk-freerateforoptionsexpiringMay21Otherrisk-freerates:4.56(June18),4.63(July16)SeeTable3.1,p.58forpricesofAOLoptionsD.M.Chance4AnIntroductiontoDerivativesandRiskManagement,6thed.
7、PrinciplesofCallOptionPricingTheMinimumValueofaCallC(S0,T,X)³0(foranycall)ForAmericancalls:Ca(S0,T,X)³Max(0,S0-X)Conceptofintrinsicvalue:Max(0,S0-X)ProofofintrinsicvalueruleforAOLcallsConceptoftimevalueSeeTable3.2,p.59fortimevaluesofAOLcallsSeeFigure3.1,
8、p.60forminimumvaluesofcallsD.M.Chance5AnIntroductiontoDerivativesandRiskManagement,6thed.PrinciplesofCallOptionPricing(continued)TheMaximumValueofaCallC(S0,T,X)£S0IntuitionSeeFigure3.2,p.61,whichaddsthistoFigure3.1TheValue
