多尺度高维亚式期权定价的奇摄动解  

Solution to multiscale Asian option pricing model with the singular perturbation method

作　　者：李惠芳[1] 包立平[1] 

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2015年第4期389-398,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(51175134)

摘　　要：讨论了一类含有快慢变换尺度的高维亚式期权定价随机波动率模型.根据Girsanov定理和Radon-Nikodym导数实现了期望回报率与无风险利率之间的转化;定义路径依赖型的新算术平均算法,借助Feynman-Kac公式,得到了风险资产期权价格所满足的相应的Black-Scholes方程,运用奇摄动渐近展开方法,得到了期权定价方程的渐近解,并得到其一致有效估计.A type of stochastic volatility model which includes fast-slow alternate multiple scales of high dimension Asian option pricing problem is discussed in this paper. According to Girsanov theorem and Radon-Nikodym, it realizes a transformation between expected return rate and no risk interest rate; Defining the new arithmetic average algorithm of path-dependent options and using Feynman-Kac＇s formula, the Black-Scholes model is formed in which the risky assets of multiscale Asian option prices. A singular perturbation expansion is used to derive an approximation for multiscale Asian option pricing equation and the uniform valid estimation is derived.

关 键 词：多尺度 亚式期权 随机波动率 奇摄动 余项估计 

分 类 号：O175.2[理学—数学]