Fourier Transforms, Option Pricing and Controls

20 Pages Posted: 10 Oct 2011  

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies

Chao Yang

AMP Financial Services

Date Written: October 9, 2011

Abstract

We incorporate a simple and effective control-variate into Fourier inversion formulas for vanilla option prices. The control-variate used in this paper is the Black-Scholes formula whose volatility parameter is determined in a generic non-arbitrary fashion. We analyze contour dependence both in terms of value and speed of convergence. We use Gaussian quadrature rules to invert Fourier integrals, and numerical results suggest that performing the contour integration along the real axis leads to the best pricing performance.

Keywords: Fourier transform, control-variate, numerical integration

Suggested Citation

Joshi, Mark S. and Yang, Chao, Fourier Transforms, Option Pricing and Controls (October 9, 2011). Available at SSRN: https://ssrn.com/abstract=1941464 or http://dx.doi.org/10.2139/ssrn.1941464

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Chao Yang

AMP Financial Services ( email )

Sydney
Australia

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