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Brownian Excursions and Parisian Barrier Options

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Marc Chesney ,
Monique Jeanblanc-Picqué  and
Marc Yor
Marc Chesney*
Affiliation:
HEC
Monique Jeanblanc-Picqué*
Affiliation:
Université d'Evry Val d'Essonne
Marc Yor*
Affiliation:
Université Pierre et Marie Curie
*
∗ Postal address: HEC, Département Finance et Economie, 1, rue de la libération, 78351 Jouy en Josas Cedex, France.
∗∗ Postal address: Equipe d'analyse et probabilités, Université d'Evry Val d'Essonne, Boulevard des Coquibus, 91025 Evry Cedex, France.
∗∗∗ Postal address: Laboratoire de Probabilités, Tour 56, 3-ième étage, Université Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex, France.
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Abstract

In this paper we study a new kind of option, called hereinafter a Parisian barrier option. This option is the following variant of the so-called barrier option: a down-and-out barrier option becomes worthless as soon as a barrier is reached, whereas a down-and-out Parisian barrier option is lost by the owner if the underlying asset reaches a prespecified level and remains constantly below this level for a time interval longer than a fixed number, called the window. Properties of durations of Brownian excursions play an essential role. We also study another kind of option, called here a cumulative Parisian option, which becomes worthless if the total time spent below a certain level is too long.

Keywords

BROWNIAN EXCURSIONBROWNIAN MEANDERBARRIER OPTIONS

MSC classification

Primary: 60G46: Martingales and classical analysis
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 1 , March 1997 , pp. 165 - 184
Copyright
Copyright © Applied Probability Trust 1997 

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