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

Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhang, You You (2016) The joint distribution of Parisian and hitting times of the Brownian motion with application to Parisian option pricing. Finance and Stochastics, 20. pp. 773-804. ISSN 0949-2984

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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.

Item Type:	Article
Official URL:	http://link.springer.com/journal/780
Additional Information:	© 2016 Springer-Verlag Berlin Heidelberg
Divisions:	Statistics
Subjects:	H Social Sciences > HG Finance Q Science > QA Mathematics
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Date Deposited:	13 Jan 2016 14:30
Last Modified:	16 Oct 2024 20:36
URI:	http://eprints.lse.ac.uk/id/eprint/64959

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