Application of the fast Gauss transform to option pricing

Application of the fast Gauss transform to option pricing

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Article ID: iaor20043297
Country: United States
Volume: 49
Issue: 8
Start Page Number: 1071
End Page Number: 1088
Publication Date: Aug 2003
Journal: Management Science
Authors: ,
Keywords: cost benefit analysis
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 requires ONN′ work when there are N′ summations to compute and the number of terms appearing in 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.

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