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Computation Of Greeks For Jump-Diffusion Models

Author

Listed:
  • M'HAMED EDDAHBI

    (Cadi Ayyad University, Faculty of Sciences and Techniques, Department of Mathematics, B.P. 549, Marrakesh 40.000, Morocco)

  • SIDI MOHAMED LALAOUI BEN CHERIF

    (Cadi Ayyad University, Faculty of Sciences and Techniques, Department of Mathematics, B.P. 549, Marrakesh 40.000, Morocco)

  • ABDELAZIZ NASROALLAH

    (Cadi Ayyad University, Faculty of Sciences and Techniques, Department of Mathematics, B.P. 549, Marrakesh 40.000, Morocco)

Abstract

In the present paper, we compute the Greeks for a class of jump diffusion models by using Malliavin calculus techniques. More precisely, the model under consideration is governed by a Brownian component and a jump part described by a compound Poisson process. Our approach consists of approximating the compound Poisson process by a suitable sequence of standard Poisson processes. The Greeks of the original model are obtained as limits or weighted limits of the Greeks of the approximate model. We illustrate our results by the computation of the Greeks for digital options in the framework of the Merton model. The technique of Malliavin weights is found to be efficient compared to the finite difference approach.

Suggested Citation

  • M'Hamed Eddahbi & Sidi Mohamed Lalaoui Ben Cherif & Abdelaziz Nasroallah, 2015. "Computation Of Greeks For Jump-Diffusion Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-30.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:06:n:s0219024915500399
    DOI: 10.1142/S0219024915500399
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