随机波动率模型下奇异期权定价的Monte Carlo方法  

Monte Carlo Method for Exotic Option Pricing Under Stochastic Volatility Model

作　　者：谷晓玉 GU Xiao-yu(School of Mathematics,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学数学学院,北京100872

出　　处：《数学的实践与认识》2023年第4期174-183,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金面上项目(12071479)。

摘　　要：Monte Carlo方法是期权定价的经典方法之一,但是收敛速度较慢.针对Hull-White随机波动率模型提出一个拟Monte Carlo方法(QMC)与对偶变量法(AV)相结合的QMCAV方法,利用该方法可以处理一些奇异期权的定价问题.应用Monte Carlo方法(MC),拟Monte Carlo方法,对偶变量法和QMCAV方法分别进行数值模拟计算,给出了在不同参数变化下回望期权与亚式期权的模拟定价.数值实验表明,QMCAV方法较MC,QMC,AV方法更加稳定有效.Monte Carlo method is one of the classical methods of option pricing,but it is convergent slowly.In this paper,QMCAV method which is combining Quasi-Monte Carlo method(QMC)with Antithetical Variable techniques(AV)is proposed to deal with the pricing of some exotic options under Hull-White stochastic volatility model.Monte Carlo(MC),Quasi-Monte Carlo,Antithetical Variable and QMCAV method are constructed for numerical simulation calculation respectively.Then,the simulation pricing of the lookback option and Asian option under different parameter variations are given.Numerical results show that the QMCAV method is more stable and effective than MC,QMC and AV methods.

关 键 词：Hull-White随机波动率模型 拟Monte Carlo方法 对偶变量法 回望期权 亚式期权 

分 类 号：F830.9[经济管理—金融学] F224