指数Lévy跳-扩散模型下欧式期权的COS定价方法  

The COS Option Pricing Method for Jump-Diffusion Models of Exponential Levy Form

作　　者：许聪聪[1] 赵芳芳 魏会贤[1] XU Cong-cong;ZHAO Fang-fang;WEI Hui-xian(Shijiazhuang Institute of Railway Technology,Shijiazhuang 050041,China;School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China)

机构地区：[1]石家庄铁路职业技术学院,河北石家庄050041 [2]山东师范大学数学与统计学院,山东济南250014

出　　处：《数学的实践与认识》2022年第1期44-52,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11801333);河北省高等学校科学技术研究重点研究项目(ZD2019080);河北省高等学校人文社科青年基金项目(SQ201095)。

摘　　要：主要研究指数Lévy形式的跳-扩散模型下欧式期权的定价问题.首先,给出了模型在均值修正等价鞅测度下的风险中性特征函数;然后,基于特征函数给出了欧式期权的傅里叶COS定价方法,并对COS方法进行修正,得到了指数Lévy形式跳-扩散模型的期权定价公式;最后,通过数值实验和实证分析检验了COS定价方法有效性,结果表明COS方法是一种稳定有效的数值方法,修正后的COS定价方法收敛速度更快、精度更高,与BS模型相比,跳-扩散模型能更精确的拟合市场数据.In this paper,we investigate the problem of option pricing under jump-diffusion models of Exponential Levy form.Firstly,the risk-neutral characteristic function of jumpdiffusion model is derived under the mean-modified equivalent martingale measure.Subsequently,we propose a corrected COS pricing method based on Fourier transform and derive the pricing formulas under jump-diffusion of the exponential Levy models.Finally,The effectiveness of the COS pricing results are tested by the numerical experiments and the empirical analysis.The results demonstrate the stability and effectivity of the COS method.Furthermore,the corrected COS pricing method shows faster convergence and higher precision than the original one.Compared with the BS model,the jump-diffusion model can fit the market data more accurately.

关 键 词：跳-扩散模型 指数Lévy模型 傅里叶变换 COS方法 期权定价 

分 类 号：F830.9[经济管理—金融学] F224