A Fast Method for Pricing Early-Exercise Options with the FFT

  • Authors:

  • R. Lord;F. Fang;F. Bervoets;C. W. Oosterlee

  • Affiliations:

  • Modeling and Research, Rabobank International, Utrecht, The Netherlands;Delft University of Technology, Delft Institute of Applied Mathematics, Delft, The Netherlands;Modeling and Research, Rabobank International, Utrecht, The Netherlands;Delft University of Technology, Delft Institute of Applied Mathematics, Delft, The Netherlands

  • Venue:
  • ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
  • Year:
  • 2007

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Abstract

A fast and accurate method for pricing early exercise options in computational finance is presented in this paper. The main idea is to reformulate the well-known risk-neutral valuation formula by recognizing that it is a convolution. This novel pricing method, which we name the `CONV' method for short, is applicable to a wide variety of payoffs and only requires the knowledge of the characteristic function of the model. As such the method is applicable within exponentially Lévy models, including the exponentially affine jump-diffusion models. For an M-times exercisable Bermudan option, the overall complexity is O(MNlog(N)) with Ngrid points used to discretize the price of the underlying asset. It is also shown that American options can be very efficiently computed by combining Richardson extrapolation to the CONV method.