Optimal Fourier Inversion in Semi-Analytical Option Pricing

Abstract:     
Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for different representations of the inverse Fourier integral. In this article, we present the optimal contour of the Fourier integral, taking into account numerical issues such as cancellation and explosion of the characteristic function. This allows for robust and fast option pricing for virtually all levels of strikes and maturities.

Keywords: Option pricing, Fourier inversion, Carr-Madan, Heston, stochastic volatility, characteristic function, damping, saddlepoint approximations

JEL Classifications: C63, G13

Working Paper Series