基于非仿射随机波动率模型的期权定价研究

中国管理科学 ›› 2013, Vol. ›› Issue (1): 1-7.

• 论文 • 下一篇

基于非仿射随机波动率模型的期权定价研究

吴鑫育¹, 杨文昱², 马超群², 汪寿阳³

1. 安徽财经大学金融学院, 安徽蚌埠 233030;
2. 湖南大学工商管理学院, 湖南长沙 410082;
3. 中国科学院数学与系统科学研究院, 北京 100190

收稿日期:2011-10-11 修回日期:2012-07-17 出版日期:2013-02-28 发布日期:2013-02-26
基金资助:
国家杰出青年科学基金项目(70825006);教育部"长江学者和创新团队发展计划"项目(IRT0916);国家自然科学基金创新研究群体科学基金项目(71221001)

Option Pricing under Non-Affine Stochastic Volatility Model

WU Xin-yu¹, YANG Wen-yu², MA Chao-qun², WANG Shou-yang³

1. School of Finance, Anhui University of Finance and Economics, Bengbu 233030, China;
2. School of Business Administration, Hunan University, Changsha 410082, China;
3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2011-10-11 Revised:2012-07-17 Online:2013-02-28 Published:2013-02-26

摘要/Abstract

摘要： 本文应用快速傅里叶变换(FFT)方法, 考虑了标的资产服从非仿射随机波动率模型下的期权定价问题。首先, 应用偏微分方程扰动分析法, 得到了标的资产对数价格分布的近似特征函数; 然后, 应用傅里叶变换及其逆变换, 推导了欧式期权的拟闭型定价公式, 对此公式应用FFT方法可以快速得到高精度数值解。数值实验表明, FFT期权定价方法是非常精确的和有效的; 最后, 给出了基于恒生指数认购权证的实证研究。实证结果表明, 非仿射随机波动率期权定价模型比经典的Black-Scholes模型具有更高的定价精确性。

关键词: 期权定价, 非仿射随机波动率, 快速傅里叶变换, 扰动法

Abstract: By applying the fast Fourier transform (FFT) method, the problem of option pricing when the underlying asset follows the non-affine stochastic volatility models is considered in this paper. Firstly, by utilizing a perturbation method to the partial differential equation of the characteristic function for the underlying log-asset price, an approximate solution for the characteristic function is derived. Then, a quasi-analytical approximate formula for European options is attained by means of Fourier transform and its inverse. This formula is easy to implement and can be accurately and quickly computed by the FFT algorithm. Numerical examples show that the FFT-based option pricing method is very accurate and efficient. Finally, an empirical study of call warrants on Hang Seng index is presented. Empirical results demonstrate that the non-affine stochastic volatility option pricing model is more accurate than the classical Black-Scholes model.

Key words: option pricing, non-affine stochastic volatility, fast Fourier transform, perturbation method

中图分类号:

F830.9

吴鑫育, 杨文昱, 马超群, 汪寿阳. 基于非仿射随机波动率模型的期权定价研究[J]. 中国管理科学, 2013, (1): 1-7.

WU Xin-yu, YANG Wen-yu, MA Chao-qun, WANG Shou-yang. Option Pricing under Non-Affine Stochastic Volatility Model[J]. Chinese Journal of Management Science, 2013, (1): 1-7.

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基于非仿射随机波动率模型的期权定价研究

Option Pricing under Non-Affine Stochastic Volatility Model

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