EFFICIENT LAPLACE INVERSION, WIENER-HOPF FACTORIZATION AND PRICING LOOKBACKS

Svetlana Boyarchenko and Sergei Levendorskiĭ ()
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Sergei Levendorskiĭ: Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 03, 1-40

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.

Keywords: Laplace inversion; Wiener-Hopf factorization; lookback option; Fourier transform; conformal deformations; parabolic inverse Fourier transform; parabolic inverse Laplace transform (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (15)

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DOI: 10.1142/S0219024913500118

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