Monte Carlo Simulation of the CGMY Process and Option Pricing
提出一种联合蒙特卡洛-傅里叶变换采样方案，用于在CGMY模型下对含无限活跃跳跃的衍生品定价，无需截断小跳跃，并通过数值实验验证了计算效率。
Abstract We present a joint Monte Carlo‐Fourier transform sampling scheme for pricing derivative products under a Carr–Geman–Madan–Yor (CGMY) model (Carr et al. [Journal of Business, 75, 305–332, 2002]) exhibiting jumps of infinite activity and finite or infinite variation. The approach relies on numerical transform inversion with computable error estimates, which allow generating the unknown cumulative distribution function of the CGMY process increments at the desired accuracy level. We use this to generate samples and simulate the entire trajectory of the process without need of truncating the process small jumps. We illustrate the computational efficiency of the proposed method by comparing it to the existing methods in the literature on pricing a wide range of option contracts, including path‐dependent univariate and multivariate products. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 34:1095–1121, 2014