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Application of the Fast Gauss Transform to Option Pricing

  • 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)

Registered author(s):

    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.49.8.1071.16405
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 49 (2003)
    Issue (Month): 8 (August)
    Pages: 1071-1088

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    Handle: RePEc:inm:ormnsc:v:49:y:2003:i:8:p:1071-1088
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