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Journal of Scientific Computing

, Volume 75, Issue 2, pp 733–761 | Cite as

A Dimension Reduction Shannon-Wavelet Based Method for Option Pricing

  • Duy-Minh Dang
  • Luis Ortiz-Gracia
Article

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.

Keywords

Shannon wavelets Dimension reduction Jump diffusions 

Mathematics Subject Classification

62P05 60E10 65T60 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsThe University of QueenslandSt Lucia, BrisbaneAustralia
  2. 2.Universitat de Barcelona School of Economics, Faculty of Economics and BusinessUniversity of BarcelonaBarcelonaSpain

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