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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Marc Jeannin & Martijn Pistorius, 2010. "Pricing And Hedging Barrier Options In A Hyper-Exponential Additive Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 657-681.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:05:n:s0219024910005954
    DOI: 10.1142/S0219024910005954
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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, August.
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