A short note on option pricing with Lévy Processes

Dominique Guegan () and Hanjarivo Lalaharison ()
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Dominique Guegan: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Hanjarivo Lalaharison: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper, we provide exact formulas for the pricing of European options under the risk neutral measure, whereas under the historic measure the data follow two types of models : a GARCH process with Lévy innovations, or a GARCH process with Poisson jumps. This approach aims to take realistic account of the jumps that are observed in the markets and to introduce them into the theory of pricing in incomplete markets. We assume that the "pricing kenel" that can move from measurement historical risk-neutral measure can be obtained from the Esscher transform (Siu et al., 1994), or using the MEMM transformation introduced by Elliott and Madam (1998). We show how these two types of "pricing kernels" impact on the options prices and through an example we quantify the difference.

Keywords: Lévy processes; pricing; incomplet markets; risk neutral measure; Processus de Lévy; marchés incomplets; mesure risque neutre (search for similar items in EconPapers)
Date: 2010-10
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00542475v1
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Published in 2010

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