基于傅立叶变换的SVJ模型的欧式期权定价  

The Evaluation of European Option Prices under Stochastic Volatility and Jump Diffusion Model Using Fourier Transform Techniques

作　　者：陈宇龙[1] 

机构地区：[1]浙江财经大学金融学院,浙江杭州310018

出　　处：《数学的实践与认识》2014年第20期39-46,共8页Mathematics in Practice and Theory

基　　金：浙江财经大学校级科研2013YJS009重点课题

摘　　要：为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.This paper investigates the valuation of European options when the underlying asset follows a jump diffusion process with stochastic volatility（SVJ）.This approach can help us to capture more accurately the option prices,but it is difficult to get the closed-form PDF of this process.To overcome the problem,a closed form representation of the characteristic function of the process is derived for the computation of European option prices via two methods of the Fourier transform.Then the numerical results from FFT will be compared with the results of Monte Carlo simulation and the B-S model.

关 键 词：随机波动模型 跳扩散模型 傅立叶变换 FFT 特征函数 

分 类 号：F830.91[经济管理—金融学] F224