Optimal Fourier Inversion in Semi-analytical Option Pricing
AbstractAt the time of writing this article, 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 almost all levels of strikes and maturities.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-066/2.
Date of creation: 27 Jul 2006
Date of revision: 05 Jun 2007
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option pricing; Fourier inversion; Carr-Madan; Heston; stochastic volatility; characteristic function; damping; saddlepoint approximations;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-08-12 (All new papers)
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- Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
- Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
- van Haastrecht, Alexander & Lord, Roger & Pelsser, Antoon & Schrager, David, 2009. "Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 436-448, December.
- Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
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