基于Tsallis分布和更新过程的欧式期权定价  

Pricing of European Option Based onTsallis Entropy and Update Process

作　　者：焦博雅 王永茂[1] JIAO Bo-ya;WANG Yong-mao(College of Science, Yanshan University, Qinhuangdao 066004, Chin)

机构地区：[1]燕山大学理学院

出　　处：《数学的实践与认识》2018年第7期95-101,共7页Mathematics in Practice and Theory

基　　金：廊坊市科技局科学技术研究项目(2016011031)

摘　　要：考虑到股价所具有的均值回复性、长记忆性和收益率尖峰后尾的特征，利用指数0-U过程和Tsallis熵分布分别对传统B-S定价模型的漂移项、随机波动项进行改进，并假设跳跃源服从比泊松过程更一般的更新过程，利用无套利思想和广义Ito公式，给出在股票价格服从一类更新跳一扩散过程下满足的偏微分方程，最后运用Feynman-Kae公式及等价鞅方法，计算欧式期权价格．Considering that the stock price has the mean reversion, long memory and the characteristics of fat-tailed, the exponential O-U process and the distribution of Tsallis entropy are used to improve the drift and random fluctuations respectively in this paper. And supposing information coming is a renewal process which is more common than Possion process, this paper deduces the partial differential equation when stock price obeys a kind of renewal jump-diffusion process using the APT theory and generalized Ito formula, at last obtains the European pricing formula by Feynman-Kac formula as well as the method of equivalent martingale.

关 键 词：期权定价 更新过程 TSALLIS熵 ITO公式 鞅 

分 类 号：F224[经济管理—国民经济] F830.9