基于随机波动率模型的路径依赖期权定价

摘要

In this paper,two typical path-dependent options are examined in the stochastic volatility framework.The underlying asset price volatility of these options is assumed to follow a fast mean-reverting stochastic process which is supported by empirical studies.The pricing of geometric average Asian call options and floating strike lookback put options is studied.By singular perturbation analysis,the corresponding partial differential equations of these two options under stochastic volatility model are obtained.The approximate prices of these two options under stochastic volatility can be expressed as two approximation terms.Analytic approximation formulas for these two path-dependent options are derived.%在随机波动率框架下,对两种典型路径依赖期权进行定价.在期权标的资产价格的波动率是一个快速均值回归随机过程的假设下,研究了几何亚式看涨期权和浮动行权价回望看跌期权这两类路径依赖期权的定价问题.通过奇异摄动分析方法,对均值回归随机波动模型的偏微分方程进行分析得到关于期权近似价格的两个近似表示项,并推导出上述两种路径依赖期权的近似解析解.