Application of the Fast Gauss Transform to Option Pricing

Mark Broadie () and Yusaku Yamamoto ()
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Mark Broadie: Graduate School of Business, Columbia University, 3022 Broadway, New York, New York, 10027-6902
Yusaku Yamamoto: Central Research Laboratory, Hitachi, Ltd., Tokyo, Japan

Management Science, 2003, vol. 49, issue 8, 1071-1088

Abstract: 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.

Keywords: Option Pricing; American Options; Fast Gauss Transform; Jump-Diffusion Model (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (22)

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