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Brownian excursions and Parisian barrier options


Chesney, Marc; Jeanblanc-Picqué, Monique; Yor, Marc (1997). Brownian excursions and Parisian barrier options. Advances in Applied Probability, 29(1):165-184.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Brownian excurison, Brownian meander, barrier options
Scope:Discipline-based scholarship (basic research)
Language:English
Date:1997
Deposited On:31 Aug 2023 13:12
Last Modified:29 Jun 2024 01:38
Publisher:Cambridge University Press
ISSN:0001-8678
OA Status:Closed
Publisher DOI:https://doi.org/10.2307/1427865
Other Identification Number:merlin-id:13230
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