导　　师： 王晓天

学科专业： 070103

授予学位： 硕士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 随着经济的发展，传统的Black—Scholes期权定价公式很难满足现实的需要，因为它是在一连串严格的假设下求得的，并没有考虑残差风险对期权定价的影响。当期权定价在考虑残差风险时，会更好的贴近实际，使定价公式更具有弹性。这对规避、管理金融风险,正确定价期权具有重要的理论及现实意义。 在离散时间交易场合，在无交易成本的假设下，高阶矩残差风险在期权定价及组合管理中起着重要的作用。本文考虑股票收益三阶矩残差风险对期权定价的影响。由平均自融资-极小方差规避规则，我们得到了含有残差风险的相应的期权价格满足的三阶偏微分方程；通过傅里叶变换，我们得到了该方程的闭式解及一阶渐近公式，我们发现当时间标度δ t收敛于零时，相应的期权定价公式收敛于Black-Scholes公式。特别地，我们得到了一般化的Delta规避策略；我们还发现投资者的风险偏好对期权定价有极其重要的影响，这在期权定价时并不能忽略。 With the development of economy, Classical Black-Scholes option pricing formula isdifficult to meet the needs of the reality, For it is obtained under a series of strict assumptions,did not consider the effect of residual risk for option pricing. When considering residual risks,it can be better close to the actual, making pricing formula more flexible. There haveimportant theoretical and practical significances to evade, manage financial risk and correctprice the options. Higher-order moments are important consideration in option pricing and in valuingportfolios under the assumption of a discrete-time trade case and absence of transaction costs.In this paper we study the impact of the stock return third-moment residual risk on Europeanoption pricing. Through mean self-financing and variance-minimizing hedging criteria wederive that the valuation of a European option satisfies a third order partial differentialequation with respect to the stock price; The closed-form solution for this partial differentialequation has been obtained by means of the Fourier transform, which will collapse to theBlock-Scholes formula as the time scaling converges to zero. In particular, we get thegeneralization of the Delta hedge strategy; we also find that the third-moment residual riskand the risk, preferences of the traders play an important role in option pricing and in portfoliohedging.

关 键 词： 期权定价 平均自融资 极小方差规则 一般化的 规避 傅里叶变换 三阶矩风险

分 类 号： [F224 F830.9]

领　　域： [经济管理] [经济管理]