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.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
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)
关键词
多尺度
亚式期权
随机波动率
奇摄动
余项估计
multiple scales
Asian options
stochastic volatility
singular perturbation
remainder term estimation
