A Dimension Reduction Shannon Wavelet-Based Method for Option Pricing

30 Pages Posted: 8 Sep 2017

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Luis Ortiz-Gracia

University of Barcelona

Date Written: May 8, 2016

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

Suggested Citation

Dang, Duy-Minh and Ortiz-Gracia, Luis, A Dimension Reduction Shannon Wavelet-Based Method for Option Pricing (May 8, 2016). Available at SSRN: https://ssrn.com/abstract=2897278 or http://dx.doi.org/10.2139/ssrn.2897278

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

Luis Ortiz-Gracia

University of Barcelona ( email )

Diagonal, 690
08034 Barcelona
Spain

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