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METHOD OF PAIRED CONTOURS AND PRICING BARRIER OPTIONS AND CDSs OF LONG MATURITIES

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  • SERGEI LEVENDORSKIĬ

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

Abstract

For prices of options with barrier and lookback features, defaultable bonds and credit default swaps (CDSs), and probability distribution functions in Lévy models, as well as for joint probability distributions of a Lévy process and its supremum or/and infimum, one can derive explicit analytical formulas in terms of inverse Laplace/Fourier transforms and the Wiener–Hopf factorization. Unless the characteristic exponent is rational, the main examples being Brownian motion, double exponential jump-diffusion and hyper-exponential jump-diffusion models, accurate numerical realization of these formulas is difficult or very time consuming, especially for options of very long and very short maturities. In this paper, a systematic approach to contour deformations in pricing formulas is developed, which greatly increases the accuracy and speed of calculations; the efficiency of the method is demonstrated with numerical examples. For options and CDSs of moderate and long maturities, much faster asymptotic formulas of comparable level of accuracy are developed.

Suggested Citation

  • Sergei Levendorskiĭ, 2014. "METHOD OF PAIRED CONTOURS AND PRICING BARRIER OPTIONS AND CDSs OF LONG MATURITIES," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-58.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:05:n:s0219024914500332
    DOI: 10.1142/S0219024914500332
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    Citations

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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, 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.
    5. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "Efficient evaluation of expectations of functions of a stable L\'evy process and its extremum," Papers 2209.12349, arXiv.org.
    6. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "L\'evy models amenable to efficient calculations," Papers 2207.02359, arXiv.org.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

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