两因素马尔可夫调制的随机波动模型下的期权定价  

Two-Factor Markov-Modulated Stochastic Volatility Models for Option Pricing

作　　者：刘雪汝 李美红 田凡 刘国祥[1] Liu Xueru;Li Meihong;Tian Fan;Liu Guoxiang(School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)

机构地区：[1]南京师范大学数学科学学院

出　　处：《南京师大学报（自然科学版）》2019年第4期31-38,共8页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(61374080)

摘　　要：研究了风险资产是由两因素马尔可夫调制的随机波动过程驱动的期权定价.第一个波动因素由CIR模型驱动,第二个波动因素、市场利率和股票回报率是由连续时间的马尔可夫过程驱动.连续时间的马尔可夫链用来描述经济状态.由两因素马尔可夫调制的随机过程描述的市场是不完全的,鞅是不唯一的.我们采用状态转换Esscher变化方法确定等价鞅测度,对欧式期权和美式期权进行定价估计,得到了欧式期权价格所满足的系统藕合偏微分方程,并导出了美式看跌期权关于欧式看跌期权和早期执行溢价的分解结果.最后给出了数值模拟结果.We consider the option pricing problem when the risky underlying assets are driven by a two-factor Morkov-modulated stochastic volatility model,with the first volatility factor driven by the Cox-Ingersoll-Ross process and the second volatility factor driven by a continuous-time hidden Markov process. The states of the Markov process can be interpreted as the unobservable states of the economy. The market described by a two-factor Markov-modulated stochastic volatility model is incomplete in general and,hence,the martingale measure is not unique. We adopt the regime switching Esscher transform to determine an equivalent martingale pricing measure. We consider the valuation of the European and American options. A system of coupled partial differential integral equations satisfied by the European option prices in derived. We also derive a decomposition result for an American put option into its European counterpart and early exercise premium. Finally,numerical illustrations are given.

关 键 词：期权定价 状态转换 Esscher变化 两因素随机波动因素 马尔可夫过程 

分 类 号：O211.9[理学—概率论与数理统计]