A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options

M. Broadie () and Y. Yamamoto ()
Additional contact information
M. Broadie: Graduate School of Business, Columbia University, 3022 Broadway, New York, New York 10027-6902
Y. Yamamoto: Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan

Operations Research, 2005, vol. 53, issue 5, 764-779

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.

Keywords: finance:; asset; pricing (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (25)

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