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

Author

Listed:
  • 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)

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.

Suggested Citation

  • M. Broadie & Y. Yamamoto, 2005. "A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options," Operations Research, INFORMS, vol. 53(5), pages 764-779, October.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:5:p:764-779
    DOI: 10.1287/opre.1050.0219
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    References listed on IDEAS

    as
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