ofRationalOptionPricing(衍生证券的定价与保值-

[e-mail]•8.1Why?Optionisaparticularlysimpletypeofcontingent-claimasset,soatheoryofoptionpricingmayleadingtogeneraltheoryofcontingent-claimspricing.8.2RestrictionsonRationalOptionPricing•Dominant:•Security(portfolio)Aisdominantoversecurity(portfolio)Bif,onsomeknowndateinthefuture,thereturnonAwillexceedthereturnonBforsomepossiblestatesoftheworld.•Assumption1:Anecessaryconditionforrationaloptionpricingtheoryisthattheoptionbepricedsuchthatitisneitheradominantnoradominatedsecurity.•Theorem8.2•IfthehypothesizedconditionsforTheorem8.1hold,anAmericanwarrantwillneverbeexercisedpriortoexpiration,andhenceithasthesamevalueasaEuropeanwarrant.•Theorem8.3•IfthehypothesizedconditionsforTheorem8.1hold,thevalueofaperpetualwarrantmustequalthevalueofthecommonstock.F对执行价格的凹性F是执行价格的减函数分布相同，起始相同，期权价值相同组合的期权价值小于期权组合的价值期权价格是标的股票风险的非减函数齐次性对标的股票价格的凹性•3121,;1,;11,;FEFEFE–8.3EffectsofDividendsandChangingExercisePrice•contents:•红利保护的条件；•红利对非红利保护期权的影响；•执行价格变动的影响。•Definition:（什么是红利保护期权。）Anoptionissaidtobepayoutprotectedif,forafixedinvestmentpolicyandfixedcapitalstructure,thevalueoftheoptionisinvarianttothechoiceofpayoutpolicy.（保证期权价值不变。）•对投资与资本结构政策实施红利保护不太可能。这两者会改变股票的风险。max0,max0,/xxsEsE•对B-S例子的反驳：对红利保护的定义不同（不重要。）•执行价格可变的情况。•提前执行只可能在红利支付前那一刻。•所以有红利支付的美式权证可以经调整的欧式权证，运用动态规划的基本思想回溯求解。1111010,;max0,,,;FSESEFSE•Corollary8.11bIfthereisafinitenumberofchangesintheexercisepriceofpayout-protectedperpetualwarrant,thenitwillnotbeexercisedanditspricewillequalthecommonstockprice.8.4RestrictionsonRationalPutOptionPricing8.5RationaloptionPricingalongBlack-ScholesLines8.6AnAlternativeDerivationoftheBlack-ScholesModel8.7ExtensionoftheModeltoincludeDividendPaymentsandExercisePriceChanges8.8ValuinganAmericanPutOption8.9Valuingthe“Down-and-out”CallOption8.10ValuingaCallableWarrant