Bates模型下一种美式期权高阶紧致有限差分定价方法  

High-Order Compact Finite Difference Scheme for Pricing American Options Under the Bates Model

作　　者：孙有发[1] 丁露涛 

机构地区：[1]广东工业大学经济与贸易学院,广州510520 [2]广东工业大学管理学院,广州510520

出　　处：《系统科学与数学》2017年第2期425-435,共11页Journal of Systems Science and Mathematical Sciences

基　　金：广东省自然科学基金项目(2014A030313514)资助课题

摘　　要：基于Jain提出的高阶紧致有限差分格式(high order compact of Jain,HOCJ),结合卷积积分(convolution integral)与快速傅里叶变换(FFT),构建了一种新颖的数值方法,简称HOCJ-CF,并用于Bates模型下美式看跌期权定价.针对期权定价偏积分微分方程(PIDE)的微分项,首先将其拆分成三个子偏微分方程(sub-PDE),然后分别应用Numerov离散方法,衍生出具有空间四阶精度和时间二阶精度的HOCJ格式;积分项则将其转化成卷积积分,并运用FFT.在相同模型参数设置下,数值结果验证了新方法在精度、收敛率及效率相比IMEX格式的优越性.In this paper, we propose a novel numerical scheme for pricing American put options under the Bates model, basing on the high-order compact discretization of Jain （HOCJ）, convolution integral and FFT. The new scheme is, namely for short, HOCJ-CF. For the differential terms of option pricing PIDE, we split them into three sub-PDEs and then apply the Numerov discretization to them, thus, deriving an HOCJ scheme with fourth-order accuracy in space and second-order in time. For the integral term, we transform it into a convolution integral which is then computed by the fast Fourier transfrom （FFT）. Numerical illustration demonstrates that, on thesame space grids, our HOCJ-CF scheme has a better accuracy, faster convergence rate and higher efficiency than the IMEX scheme under the same model settings.

关 键 词：关键词美式期权定价 高阶紧致格式 FFT Numerov离散 傅里叶变换 卷积积分 Bates 模型. 

分 类 号：F830.9[经济管理—金融学] O241.82[理学—计算数学]