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Pricing And Hedging Barrier Options In A Hyper-Exponential Additive Model

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Author Info

  • MARC JEANNIN

    ()
    (Models and Methodology Group, Risk Management Department, Nomura International plc, Nomura House 1 St Martin's-le-Grand, London EC1A 4NP, UK)

  • MARTIJN PISTORIUS

    ()
    (Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK)

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    Abstract

    In this paper, we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability. The solution rests on a randomization and an explicit matrix Wiener-Hopf factorization. Employing this result we derive explicit expressions for the Laplace-Fourier transforms of the prices and Greeks of barrier options. As a numerical illustration, the prices and Greeks of down-and-in digital and down-and-in call options are calculated for a set of parameters obtained by a simultaneous calibration to Stoxx50E call options across strikes and four different maturities. By comparing the results with Monte-Carlo simulations, we show that the method is fast, accurate, and stable.

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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): 13 (2010)
    Issue (Month): 05 ()
    Pages: 657-681

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    Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:05:p:657-681

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    Related research

    Keywords: Hyper-exponential additive processes; matrix Wiener-Hopf factorization; first passage times; barrier options; multi-dimensional Laplace transform; Fourier transform; sensitivities;

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