【作者】 张增林；

【导师】 蹇明；

【作者基本信息】 华中科技大学 ， 应用数学， 2007， 硕士

【摘要】 在金融市场中，路径依赖型期权因其路径依赖的特征而比标准期权更具有竞争优势，从而日益成为期权定价领域的研究热点．CEV模型是几何布朗运动的推广，近年来CEV模型下路径依赖型期权的定价研究主要集中在回望期权和障碍期权，而冷落了同样具有路径依赖特征的亚式期权．本文主要考虑了两个问题：标的资产服从CEV过程时几何平均亚式期权的定价和B-S模型下具有浮动敲定价格的算术平均亚式期权的定价．首先，阐述了标准几何亚式期权的涵义及其模型，介绍CED的涵义，借助Phelim P．Boyle和Yisong Tian为CEV模型下回望期权和障碍期权的定价技巧，利用二叉树逼近方法得到服从CEV过程且有离散红利支付几何亚式期权的定价。然后将几何平均的权数推广到更一般的加权几何平均，得到CEV过程下有离散红利支付的加权几何平均亚式期权的定价。其次，考虑了B-S模型下具有浮动敲定价格的算术平均亚式期权的定价问题．为简化二叉树方法中繁琐的计算量，我们在已有的线性插值的基础上引入抛物插值方法。利用二叉树方法和抛物插值方法的结合得出了具有浮动敲定价格的算术平均亚式期权的近似定价。最后给出了实例分析，验证了二叉树方法的有效性及收敛性，同时证明了抛物插值具有比线性插值更快的收敛速度．更多还原

【Abstract】 In the financial market, path-dependent option is more competitive than standardoption profit from its path-dependent character, and increasingly become the researcher’sfocus of the option pricing field. CEV model is the generalization of the Geometric Brown-ian motion, the option pricing research under CEV process mainly focuses on lookbackoptions and barrier options, but ignores the Asian options which is also path-dependent.In this paper we consider two problems on Asian option pricing: pricing geometricAsian option on underlying assets obeying CEV process; pricing arithmetic average Asianoption with ?oating strike price under B-S model.Firstly, standard geometric Asian option and its pricing model are considered, thenCEV is introduced. By virtue of the technique Phelim P.Boyle and Yisong Tian usedto price lookback options and barrier options under CEV process, the application of abinomial tree is put forward to get the price of the geometric Asian option with discretedividend paid under CEV process. Besides, we extend the geometric average weightnumber to the more commonly weighted geometric average.Secondly, we consider the pricing of the arithmetic average Asian option with ?oatingstrike price under B-S model. In order to simplify the fussy computation in the binomialtree method, we introduce the Parabolic interpolation on the basis of the existed linearinterpolation. By the combine of the binomial tree method and the Parabolic interpo-lation, we obtained the approximate price of the arithmetic average Asian option with?oating strike price. In the end, we present the instance analysis, validate the validityand astringency of the binomial tree method, at the same time proved that the parabolicinterpolation is more e?cient than the linear interpolation.更多还原