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Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided L�vy models: the parabolic Laplace inversion method

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  • Mitya Boyarchenko
  • Sergei Levendorskiĭ

Abstract

Recently, the advantages of conformal deformations of the contours of integration in pricing formulas were demonstrated in the context of wide classes of L�vy models and the Heston model. In the present paper, we construct efficient conformal deformations of the contours of integration in the pricing formulas for barrier options and CDS in the setting of spectrally one-sided L�vy models, taking advantage of Rogers's trick [ J. Appl. Prob. , 2000, 37 , 1173-1180] that greatly simplifies calculation of the Wiener-Hopf factors. We extend the trick to wide classes of L�vy processes of infinite variation with zero diffusion component. In the resulting formulas (both in the finite variation and the infinite variation cases), we make quasi-parabolic deformations as in Boyarchenko and Levendorskiĭ [ Int. J. Theor. Appl. Finance , 2013, 16 (3), 1350011], which greatly increase the rate of convergence of the integrals. We demonstrate that in many cases the proposed method is more accurate than the standard realization of Laplace inversion. We also exhibit examples in which the standard realization is so unstable that it cannot be used for any choice of the error control parameters. This may lead to a ghost calibration : a situation where a parameter set of a model is declared to be a 'good fit' to the data only because the errors of calibration and of the numerical method used for pricing (almost) cancel each other out.

Suggested Citation

  • Mitya Boyarchenko & Sergei Levendorskiĭ, 2015. "Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided L�vy models: the parabolic Laplace inversion method," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 421-441, March.
  • Handle: RePEc:taf:quantf:v:15:y:2015:i:3:p:421-441
    DOI: 10.1080/14697688.2014.941914
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    References listed on IDEAS

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    1. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    2. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    3. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    4. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    5. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
    6. Tim Leung & Kazutoshi Yamazaki, 2013. "American step-up and step-down default swaps under L�vy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 137-157, January.
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    8. Marco De Innocentis & Sergei Levendorskiĭ, 2013. "Pricing discrete barrier options and credit default swaps under L�vy processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1337-1365, July.
    9. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    10. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    11. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, August.
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    Cited by:

    1. Semere Habtemicael & Indranil SenGupta, 2016. "Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-35, December.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2022. "L\'evy models amenable to efficient calculations," Papers 2207.02359, arXiv.org.
    8. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.

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