广义CEV模型下分数阶BS方程的欧式期权定价及反问题  

Pricing and Inverse Problem of European Options for Fractional Order BS Equations Under the Generalized CEV Model

作　　者：许作良 沈诺晨 XU Zuo-liang;SHEN Nuo-chen(School of Mathematics,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学数学学院,北京100872

出　　处：《数学的实践与认识》2025年第2期169-179,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12071479)。

摘　　要：文章主要研究广义CEV模型下分数阶Black-Scholes方程的欧式期权定价及反问题.首先结合CEV扩散过程和分数阶模型提出了带有分红的广义CEV波动率模型,推导出欧式期权满足的定价公式.其次在空间和时间上进行差分离散,并进行了数值模拟以验证模型的有效性.最后讨论了该模型下欧式期权的波动率反演问题,利用线性化方法进行求解,并结合中国期权市场进行了实证分析,反演得出弹性系数.This article mainly studies the pricing and inverse problem of European options for fractional order Black Scholes equations under the generalized CEV model.Firstly,the pricing problem of fractional order Black Scholes equations combined with European options under the generalized CEV model is introduced.Based on the generalized CEV volatility model with dividends proposed by Cox and Jumarie,the pricing formula satisfied by European options is derived.Secondly,the difference is dispersed in space and time,and the effectiveness of the model is verified through numerical simulation.Finally,the pricing and inverse problem of fractional order Black Scholes equation European options under the generalized CEV model were discussed,and numerical experiments were conducted.Empirical analysis was conducted in conjunction with the Chinese options market,and the elasticity coefficient was inverted.

关 键 词：广义CEV模型 分数阶BS方程 期权定价 反问题 

分 类 号：F83[经济管理—金融学]