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Efficient Laplace Inversion, Wiener-Hopf Factorization And Pricing Lookbacks

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  • SVETLANA BOYARCHENKO

    (Department of Economics, University of Texas at Austin, 1 University Station C3100, Austin, TX 78712–0301, USA)

  • SERGEI LEVENDORSKIĬ

    (Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom)

Abstract

We construct fast and accurate methods for (a) approximate Laplace inversion, (b) approximate calculation of the Wiener-Hopf factors for wide classes of Lévy processes with exponentially decaying Lévy densities, and (c) approximate pricing of lookback options. In all cases, we use appropriate conformal change-of-variable techniques, which allow us to apply the simplified trapezoid rule with a small number of terms (the changes of variables in the outer and inner integrals and in the formulas for the Wiener-Hopf factors must be compatible in a certain sense). The efficiency of the method stems from the properties of functions analytic in a strip (these properties were explicitly used in finance by Feng and Linetsky 2008). The same technique is applicable to the calculation of the pdfs of supremum and infimum processes, and to the calculation of the prices and sensitivities of options with lookback and barrier features.

Suggested Citation

  • Svetlana Boyarchenko & Sergei Levendorskiĭ, 2013. "Efficient Laplace Inversion, Wiener-Hopf Factorization And Pricing Lookbacks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 1-40.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:03:n:s0219024913500118
    DOI: 10.1142/S0219024913500118
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    References listed on IDEAS

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    1. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, September.
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    Cited by:

    1. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2020. "Static and semistatic hedging as contrarian or conformist bets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 921-960, July.
    2. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Efficient evaluation of joint pdf of a L\'evy process, its extremum, and hitting time of the extremum," Papers 2312.05222, arXiv.org.
    3. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models," Papers 2312.03915, arXiv.org.
    4. Sergei Levendorskiĭ, 2022. "Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems," Mathematics, MDPI, vol. 10(7), pages 1-36, March.
    5. Sergei Levendorskiĭ, 2017. "ULTRA-FAST PRICING BARRIER OPTIONS AND CDSs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-27, August.
    6. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "L\'evy models amenable to efficient calculations," Papers 2207.02359, arXiv.org.
    7. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    8. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient evaluation of double-barrier options and joint cpdf of a L\'evy process and its two extrema," Papers 2211.07765, arXiv.org.
    9. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    10. Svetlana Boyarchenko & Sergei Levendorskiä¬ & J. Lars Kyrkby & Zhenyu Cui, 2021. "Sinh-Acceleration For B-Spline Projection With Option Pricing Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(08), pages 1-50, December.
    11. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient inverse $Z$-transform and pricing barrier and lookback options with discrete monitoring," Papers 2207.02858, arXiv.org, revised Jul 2022.
    12. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing," Papers 2002.09911, arXiv.org.
    13. Weinan Zhang & Pingping Zeng, 2023. "A transform-based method for pricing Asian options under general two-dimensional models," Quantitative Finance, Taylor & Francis Journals, vol. 23(11), pages 1677-1697, November.

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