关于欧式期权定价若干问题的研究

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1、华中科技大学硕士学位论文摘要本文考虑了欧式期权定价方面的三个问题:有交易费和随机分红时的欧式期权定价价.股票收益服从Ornstein-Uhlenbeck过程的期权定价和随机利率下的外汇期权定首先在无套利框架下考虑了股票有离散随机分红且股票交易收取与股票价格成比例交易费时的欧式期权定价,并给出了显式表达式.它是标的资产为远期的看涨期权定价公式的一种简单推广(当交易费和分红为零时为标的资产远期合约的欧式期权定价公式)结果表明期权价格随交易费的增加而增加随分红的增加而减少.本文阐明公司股票和债券是基于公司资产上的期权运用期权理论给股票债券定价分析了股东和债权人之间的利益关系并

2、讨论了公司证券对期权价值的影响.其次讨论了股票价格服从几何布朗运动股票收益服从Ornstein-Uhlenbeck过程的欧式期权定价问题利用无套利原理给出了期权价格满足的偏微分方程并运用傅立叶逆变换求出了欧式看涨期权定价公式的封闭解.最后考虑了三种风险资源本国期限结构风险外国期限结构风险和汇率风险.在随机利率情况下利用鞅方法讨论了外汇欧式期权的定价问题得到了欧式看涨期权和看跌期权价格的解析表达式及其评价关系并考虑了期权的套期保值问题.关键词期权定价随机分红交易费随机利率外汇I华中科技大学硕士学位论文AbstractInthispaperweconsi

3、derthreeproblemsonEuropeanoptionpricing:Europeanoptionpricingwithtransactioncostsandstochasticdividends;optionpricingwithstockreturnfollowingOrnstein-Uhlenbeckprocess;optionpricingonforeigncurrencyunderstochasticinterestrate.Firstly,weconsiderpricingEuropeanoptionproblemswithtransactioncosts

4、whichareproportionaltostocks’valueanddiscretestochasticdividendsofstocksunderanarbitrage-freeframeworkandgiveanexplicitexpressionofoptionpricingformula,whichextendsoptionpricingformulawhereunderlyingassetsareforwardcontracts.(whenbothtransactioncostsanddividendsbecomezero,itreducestotheopti

5、onpricingformulawhereunderlyingassetsareforwardcontracts).Theresultindicatesthatoptionpriceincreasesastransactioncostsofstocksincreaseanddecreasesasdividendsofstocksincrease.Itdemonstratesthatcorporatestocksandbondsareoptionsbasedoncorporateassets.Andthenweapplyoptiontheorytopricestocksandbo

6、nds.Theinterestrelationshipbetweenshareholdersandloanersisanalyzedandcorporatesecurity’seffectsonoptionpricearediscussed.Secondly,EuropeanoptionpricingproblemisdiscussedwhenpriceofstocksfollowsgeometricBrownmotionandreturnofstocksfollowsOrnstein-Uhlenbeckprocess.UsingArbitrage-freeprinciple,

7、wegiveapartialdifferentialequationwithwhichoptionpriceissatisfiedandusingFourierinversetransformation,theclosed-formsolutiontoEuropeanCalloptionpricingformulaisgiven.Finally,weconsiderthreeriskresources:domestictermstructurerisk;foreigntermstructur