Fourier Transforms, Option Pricing and Controls

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.

Number of Pages in PDF File: 20

Keywords: Fourier transform, control-variate, numerical integration

working papers series