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高校应用数学学报
高校应用数学学报  2015, Vol. 30 Issue (4): 389-398    
    
多尺度高维亚式期权定价的奇摄动解
李惠芳, 包立平
杭州电子科技大学 理学院, 浙江杭州 310018
Solution to multiscale Asian option pricing model with the singular perturbation method
LI Hui-fang, BAO Li-ping
The school of Science, Hangzhou Dianzi University, Hangzhou 310018, China
 全文: PDF 
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.
关键词： 多尺度;  亚式期权;  随机波动率;  奇摄动;  余项估计    
Abstract: 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.
Key words: multiple scales    Asian options    stochastic volatility    singular perturbation    remainder term estimation
收稿日期: 2015-06-11 出版日期: 2018-05-19
CLC:  O175.2  
基金资助: 国家自然科学基金(51175134)
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引用本文:

李惠芳, 包立平. 多尺度高维亚式期权定价的奇摄动解[J]. 高校应用数学学报, 2015, 30(4): 389-398.

LI Hui-fang, BAO Li-ping. Solution to multiscale Asian option pricing model with the singular perturbation method. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 389-398.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2015/V30/I4/389

[1] 包立平. 一类具有不连续源的奇摄动半线性微分方程组边值问题[J]. 高校应用数学学报, 2017, 32(4): 413-422.
[2] 包立平. 一类奇摄动半线性时滞抛物型偏微分方程的渐近解[J]. 高校应用数学学报, 2016, 31(3): 307-315.
[3] 李志广, 康淑瑰. 非线性Black-Scholes模型下几何平均亚式期权定价[J]. 高校应用数学学报, 2016, 31(1): 39-49.