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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.
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