COMPUTATION OF GREEKS FOR JUMP-DIFFUSION MODELS

M'Hamed Eddahbi (), Sidi Mohamed Lalaoui Ben Cherif () and Abdelaziz Nasroallah ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 06, 1-30

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.

Keywords: Greeks; sensitivity analysis; jump-diffusion models; compound poisson process; Malliavin calculus; Monte Carlo methods (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219024915500399

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