Optimal Fourier Inversion in Semi-Analytical Option Pricing

Tinbergen Institute Discussion Paper No. 2006-066/2

21 Pages Posted: 3 Aug 2006

See all articles by Roger Lord

Roger Lord

Cardano Risk Management

Christian Kahl

Commerzbank Corporates & Markets; University of Wuppertal; ABN-Amro Bank, United Kingdom

Date Written: May 10, 2007


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 Classification: C63, G13

Suggested Citation

Lord, Roger and Kahl, Christian, Optimal Fourier Inversion in Semi-Analytical Option Pricing (May 10, 2007). Tinbergen Institute Discussion Paper No. 2006-066/2, Available at SSRN: https://ssrn.com/abstract=921336 or http://dx.doi.org/10.2139/ssrn.921336

Roger Lord (Contact Author)

Cardano Risk Management ( email )

Rotterdam 3011 AA

Christian Kahl

Commerzbank Corporates & Markets ( email )

60 Gracechurch Street
London, EC3V 0HR
United Kingdom

University of Wuppertal ( email )

Gaußstraße 20
42097 Wuppertal

ABN-Amro Bank, United Kingdom ( email )

London EC2N 4BN
United Kingdom

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