随机波动率与跳模型下股价的分析与模拟

吉林大学学报(理学版)

随机波动率与跳模型下股价的分析与模拟

曹桂兰, 周媛

中国科学院大学数学科学学院, 北京 100190

收稿日期:2015-09-16 出版日期:2016-03-26 发布日期:2016-03-23
通讯作者: 周媛 E-mail:zhouyuan0414@163.com

Analysis and Simulation of Stock Price in aStochastic Volatility Model with Jumps

CAO Guilan, ZHOU Yuan

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

Received:2015-09-16 Online:2016-03-26 Published:2016-03-23
Contact: ZHOU Yuan E-mail:zhouyuan0414@163.com

摘要/Abstract

摘要：

运用随机微分方程和Monte Carlo模拟, 建立并检验带Poisson跳且波动率服从CIR过程的股票价格模型, 给出了该模型下股票价格的表达式及股票收益率的均值和方差. 数值计算表明, 该模型下股票的收益率更具尖峰厚尾的特征.

关键词: 随机波动率, 复合Poisson过程, CIR过程, Monte Carlo精确模拟

Abstract:

Using stochastic differential equation and Monte Carlo simulation, we established and verified a stock price model with Poisson jumps when the volatility obeyed CIR process. The price formula of stock was given and we also computed the mean and variance of stock yield. Numerical result indicates that the model can better reflect the characteristics of high kurtosis and fat tail of stock yields distribution.

Key words: stochastic volatility, compound Poisson process, CIR process, Monte Carlo exact simulation

中图分类号:

O211.9

曹桂兰, 周媛. 随机波动率与跳模型下股价的分析与模拟[J]. 吉林大学学报(理学版), 2016, 54(02): 257-265.

CAO Guilan, ZHOU Yuan. Analysis and Simulation of Stock Price in aStochastic Volatility Model with Jumps[J]. Journal of Jilin University Science Edition, 2016, 54(02): 257-265.