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 the same 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.