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Prices And Sensitivities Of Barrier And First-Touch Digital Options In Lévy-Driven Models

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Author Info

  • MITYA BOYARCHENKO

    ()
    (Department of Mathematics, University of Michigan, 530 Church Street, 2704 East Hall, Ann Arbor, MI 48109-1043, USA)

  • SERGEI LEVENDORSKIĬ

    ()
    (Department of Mathematics, The University of Leicester, University Road, Leicester LE1 7RH, UK)

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    Abstract

    We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Lévy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the results obtained using other (sometimes fundamentally different) approaches that exist in the literature. However, our method is computationally much faster (often, dozens of times faster). Moreover, our technique has the advantage that its application does not entail a detailed analysis of the underlying Lévy process: one only needs an explicit analytic formula for the characteristic exponent of the process. Thus our algorithm is very easy to implement in practice. Finally, our method yields accurate results for a wide range of values of the spot price, including those that are very close to the barrier, regardless of whether the maturity period of the option is long or short.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 12 (2009)
    Issue (Month): 08 ()
    Pages: 1125-1170

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    Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:08:p:1125-1170

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    Related research

    Keywords: Option pricing; greeks; barrier options; first-touch digitals; Lévy processes; Fast Fourier transform; Carr's randomization; KoBoL processes; CGMY model; Normal Inverse Gaussian processes; Variance Gamma processes; Wiener–Hopf factorization;

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    Cited by:
    1. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
    2. Federico De Olivera & Ernesto Mordecki, 2014. "Computing Greeks for L\'evy Models: The Fourier Transform Approach," Papers 1407.1343, arXiv.org.

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