Title: On convergence of the utility indifference pricing in the model preserving the CGMY minimal entropy martingale measure

Authors: Imen Ben Abdelwahed; Faouzi Trabelsi

Addresses: Faculté des Sciences de Monastir, Department of mathematics, Unité de Recherche 'Ondelettes Et Multifractales' (99UR1504), Université de Monastir, Avenue de l’Environnement – Monastir – 5000, Tunisia ' Department of Mathematics, Institut Supérieur d'Informatique et de Mathématiques de Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Tunisia; Faculté des Sciences de Monastir, Unité de Recherche 'Ondelettes Et Multifractales' (99UR1504), Université de Monastir, Avenue de l'Environnement – Monastir – 5000, Tunisia

Abstract: Motivated by financial instrument for pricing and hedging and also by the field of risk management, we consider measure changes for CGMY Lévy processes which stay in the CGMY class. Within this two-parametric Esscher class of measure changes, we focus on the martingale measure with minimal relative entropy, called 'model preserving minimal entropy martingale measure' (MPMEMM). We link this measure to the utility-based indifference pricing. We precisely show that for bounded payoffs, the (exponential) utility indifference price goes to the option's price evaluated under the MPMEMM as the Arrow-Pratt measure of absolute risk aversion goes to zero. We also show that the class of Esscher martingale measures preserving the CGMY character is reduced to a single measure, described in full detail. Our results are new and contribute to the theory of option pricing under Lévy models.

Keywords: CGMY process; equivalent martingale measures; EMMs; relative entropy; two-parametric Esscher martingale measure; model preserving MEMM; minimal entropy martingale measure; MPMEMM; duality relation; utility indifference pricing; hedging; risk management; option pricing; risk aversion.

DOI: 10.1504/IJMOR.2015.070197

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.4, pp.428 - 463

Received: 18 Dec 2013
Accepted: 15 Feb 2014
Published online: 29 Jun 2015 *

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