A double-exponential fast Gauss transform algorithm for pricing discrete path-dependent options

A double-exponential fast Gauss transform algorithm for pricing discrete path-dependent options

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Article ID: iaor2008814
Country: United States
Volume: 53
Issue: 5
Start Page Number: 764
End Page Number: 779
Publication Date: Sep 2005
Journal: Operations Research
Authors: ,
Keywords: numerical analysis
Abstract:

This paper develops algorithms for the pricing of discretely sampled barrier, lookback, and hindsight options and discretely exercisable American options. Under the Black–Scholes framework, the pricing of these options can be reduced to evaluation of a series of convolutions of the Gaussian distribution and a known function. We compute these convolutions efficiently using the double-exponential integration formula and the fast Gauss transform. The resulting algorithms have computational complexity of O(nN), where the number of monitoring/exercise dates is n and the number of sample points at each date is N, and our results show the error decreases exponentially with N. We also extend the approach and provide results for Merton's lognormal jump-diffusion model.

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