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Finance and Stochastics
Published in: Finance and Stochastics 3/2016

01-07-2016

The joint distribution of Parisian and hitting times of Brownian motion with application to Parisian option pricing

Authors: Angelos Dassios, You You Zhang

Published in: Finance and Stochastics | Issue 3/2016

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Abstract

We study the joint law of Parisian time and hitting time of a drifted Brownian motion by using a three-state semi-Markov model, obtained through perturbation. We obtain a martingale to which we can apply the optional sampling theorem and derive the double Laplace transform. This general result is applied to address problems in option pricing. We introduce a new option related to Parisian options, being triggered when the age of an excursion exceeds a certain time or/and a barrier is hit. We obtain an explicit expression for the Laplace transform of its fair price.
previous article Almost-sure hedging with permanent price impact
next article Retraction Note to: The distribution of the maximum of a variance gamma process and path-dependent option pricing

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Appendix
Available only for authorised users
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Metadata
Title
The joint distribution of Parisian and hitting times of Brownian motion with application to Parisian option pricing
Authors
Angelos Dassios
You You Zhang
Publication date
01-07-2016
Publisher
Springer Berlin Heidelberg
Published in
Finance and Stochastics / Issue 3/2016
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI
https://doi.org/10.1007/s00780-016-0302-6

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