Application of the fast Gauss transform to option pricing

• 成果类型: Article
• 署名作者: Broadie, M; Yamamoto, Y
• 署名单位: Columbia University; Hitachi Limited
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.49.8.1071.16405
• 发表日期: 2003
• 页码: 1071-1088
• 关键词: Option pricing; American options; fast Gauss transform; jump-diffusion model

摘要

In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requires O(NN') work when there are N' summations to compute and the number of terms appearing m each summation is N, we can reduce the amount of work to O(N + N') by using a technique called the fast Gauss transform. In this paper, we apply this technique to the multinomial method and the stochastic mesh method, and show by numerical experiments how it can speed up these methods dramatically, both for the Black-Scholes model and Merton's lognormal jump-diffusion model. We also propose extensions of the fast Gauss transform method to models with non-Gaussian densities.