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A Dimension Reduction Shannon-Wavelet Based Method for Option Pricing

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Abstract

We present a robust and highly efficient dimension reduction Shannon-wavelet method for computing European option prices and hedging parameters under a general jump-diffusion model with square-root stochastic variance and multi-factor Gaussian interest rates. Within a dimension reduction framework, the option price can be expressed as a two-dimensional integral that involves only (i) the value of the variance at the terminal time, and (ii) the time-integrated variance process conditional on this value. A Shannon wavelet inverse Fourier technique is developed to approximate the conditional density of the time-integrated variance process. Furthermore, thanks to the excellent approximation properties of Shannon wavelets, the overall pricing procedure is reduced to the evaluation of just a single integral that involves only the density of the terminal variance value. This single integral can be accurately evaluated, since the density of the variance at the terminal time is known in closed-form. We develop sharp approximation error bounds for the option price and hedging parameters. Numerical experiments confirm the robustness and impressive efficiency of the method.

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Notes

  1. A stochastic factor is usually understood as a source of randomness which is typically modelled by a Brownian motion.

  2. Having a non-trivial correlation between the underlying asset price and its variance is important for capturing the skewness in the underlying asset price.

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Authors and Affiliations

  1. School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, 4072, Australia

    Duy-Minh Dang

  2. Universitat de Barcelona School of Economics, Faculty of Economics and Business, University of Barcelona, John M. Keynes 1-11, 08034, Barcelona, Spain

    Luis Ortiz-Gracia

Authors
  1. Duy-Minh Dang
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  2. Luis Ortiz-Gracia
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Correspondence to Duy-Minh Dang.

Additional information

This research was supported in part by a University of Queensland Early Career Researcher (ECR) Grant (Grant No. 1006301-01-298-21-609775), and by the Agència de Gestió i d’Ajuts Universitaris i de Recerca (Grant No. 2014SGR-1307).

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Dang, DM., Ortiz-Gracia, L. A Dimension Reduction Shannon-Wavelet Based Method for Option Pricing. J Sci Comput 75, 733–761 (2018). https://doi.org/10.1007/s10915-017-0556-y

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  • DOI: https://doi.org/10.1007/s10915-017-0556-y

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