基于非仿射随机波动率模型的期权定价研究

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。

Option Pricing under Non-Affine Stochastic Volatility Model

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.