Application of the Fast Gauss Transform to Option Pricing
提出将快速高斯变换应用于美式期权定价的多项式和随机网格方法，大幅降低计算量，并通过数值实验验证其在Black-Scholes和跳跃扩散模型中的加速效果。
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 requiresO(NN') work when there areN' summations to compute and the number of terms appearing in each summation isN, we can reduce the amount of work toO(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.