基于CEV模型期权定价问题的分析

发布时间：2018-02-14 10:18

本文关键词： CEV模型转移概率密度函数 Kolmogorov后向方程期权定价有限差分方法　出处：《浙江大学》2012年硕士论文　论文类型：学位论文

【摘要】：期权定价问题一直是金融行业比较热门的课题,本文通过对经典的CEV模型进行了分析,利用Kolmogorov前向方程和Feller引理得到标的资产在该模型下的期权定价公式,之后又对该模型下几种不同参数下的期权定价问题进行了分析,并得到了相应的期权定价公式,在其中也包括对经典的Black-Scholes模型的期权定价公式的推导。在原始的CEV模型的基础之上,对CEV模型进行了简单的变形,通过考虑变形后随机微分方程的Kolmogorov后向方程,并借助于有限差分的显示方法,得到在该模型下的期权定价的数值解,并对在变形之后模型下影响欧式期权的主要因素进行了分析。在文章的最后,我们对变形的模型进行了实验验证,通过对美式看跌期权的定价进行实例研究,并得到了很好的效果。
[Abstract]:Option pricing has always been a hot topic in financial industry. This paper analyzes the classical CEV model and obtains the option pricing formula of underlying assets under this model by using Kolmogorov forward equation and Feller Lemma. Then, the option pricing problem under different parameters is analyzed, and the corresponding option pricing formula is obtained. It also includes the derivation of the option pricing formula of the classical Black-Scholes model. On the basis of the original CEV model, the CEV model is simply deformed, and the Kolmogorov backward equation of the stochastic differential equation after the deformation is considered. With the help of the finite-difference display method, the numerical solution of option pricing under the model is obtained, and the main factors influencing the European option under the deformed model are analyzed. We have carried on the experimental verification to the deformation model, through the example research to the American put option pricing, and obtained the very good result.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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