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The Smooth-Fit Property in an Exponential Lévy Model

Part of: Stochastic processes Mathematical finance Markov processes

Published online by Cambridge University Press:  04 February 2016

Damien Lamberton  and
Mohammed Mikou
Damien Lamberton*
Affiliation:
Université Paris-Est
Mohammed Mikou*
Affiliation:
Ecole Internationale des Sciences du Traitement de l'Information
*
∗ Postal address: Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR CNRS 8050, 5 Boulevard Descartes, F-77454 Marne-la-Vallée Cedex 2, France. Email address: damien.lamberton@univ-mlv.fr
∗∗ Postal address: Laboratoire de Mathématiques, Ecole Internationale des Sciences du Traitement de l'Information, avenue du Parc, 95011 Cergy-Pontoise Cedex, France. Email address: mohammed.mikou@eisti.eu
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Abstract

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We study the smooth-fit property of the American put price with finite maturity in an exponential Lévy model when the underlying stock pays dividends at a continuous rate. As in the perpetual case, a regularity property is sufficient for smooth fit to occur. We also derive conditions on the Lévy measure under which smooth fit fails.

Keywords

Optimal stoppingLévy processsmooth-fit propertyAmerican option

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G51: Processes with independent increments; L'evy processes 91G20: Derivative securities
Secondary: 60J75: Jump processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 137 - 149
Copyright
© Applied Probability Trust 

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