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Optimal Fourier Inversion in Semi-analytical Option Pricing

Author

Listed:
  • Roger Lord

    (Erasmus Universiteit Rotterdam, and Rabobank International)

  • Christian Kahl

    (University of Wuppertal, and ABN AMRO, London)

Abstract

At 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.

Suggested Citation

  • Roger Lord & Christian Kahl, 2006. "Optimal Fourier Inversion in Semi-analytical Option Pricing," Tinbergen Institute Discussion Papers 06-066/2, Tinbergen Institute, revised 05 Jun 2007.
    • Handle: RePEc:tin:wpaper:20060066
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
    3. Alessandro Ramponi, 2016. "On a Transform Method for the Efficient Computation of Conditional V@R (and V@R) with Application to Loss Models with Jumps and Stochastic Volatility," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 575-596, June.
    4. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
    5. Stefan Gerhold & Christoph Gerstenecker & Arpad Pinter, 2019. "Moment explosions in the rough Heston model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 575-608, December.
    6. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    7. G. Mazzei & F. G. Bellora & J. A. Serur, 2021. "Delta Hedging with Transaction Costs: Dynamic Multiscale Strategy using Neural Nets," Papers 2109.12337, arXiv.org.
    8. Bravo, Jorge M. & Nunes, João Pedro Vidal, 2021. "Pricing longevity derivatives via Fourier transforms," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 81-97.
    9. 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.
    10. Sigurd Emil Rømer & Rolf Poulsen, 2020. "How Does the Volatility of Volatility Depend on Volatility?," Risks, MDPI, vol. 8(2), pages 1-18, June.
    11. Carlo Marinelli & Stefano D'Addona, 2024. "On the relative performance of some parametric and nonparametric estimators of option prices," Papers 2412.00135, arXiv.org.
    12. Stavros J. Sioutis, 2017. "Calibration and Filtering of Exponential L\'evy Option Pricing Models," Papers 1705.04780, arXiv.org.
    13. Martin Forde & Stefan Gerhold & Benjamin Smith, 2019. "Small-time, large-time and $H\to 0$ asymptotics for the Rough Heston model," Papers 1906.09034, arXiv.org, revised Oct 2020.
    14. Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Michael Samet & Ra'ul Tempone, 2024. "Quasi-Monte Carlo for Efficient Fourier Pricing of Multi-Asset Options," Papers 2403.02832, arXiv.org.
    15. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    16. Pingping Zeng & Yue Kuen Kwok, 2016. "Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1375-1391, September.
    17. Reza Doostaki & Mohammad Mehdi Hosseini, 2022. "Option Pricing by the Legendre Wavelets Method," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 749-773, February.
    18. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.
    19. Fabien Le Floc'h, 2020. "Notes on the SWIFT method based on Shannon Wavelets for Option Pricing," Papers 2005.13252, arXiv.org.
    20. Gong, Xiao-li & Zhuang, Xin-tian, 2016. "Option pricing and hedging for optimized Lévy driven stochastic volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 118-127.
    21. François M. Quittard-Pinon & Rivo Randrianarivony, 2010. "Exchange Options when One Underlying Price Can Jump," Finance, Presses universitaires de Grenoble, vol. 31(1), pages 33-53.
    22. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    23. Stefan Gerhold & Christoph Gerstenecker & Arpad Pinter, 2018. "Moment Explosions in the Rough Heston Model," Papers 1801.09458, arXiv.org, revised Apr 2018.

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    More about this item

    Keywords

    option pricing; Fourier inversion; Carr-Madan; Heston; stochastic volatility; characteristic function; damping; saddlepoint approximations;
    All these keywords.

    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

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