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

Dassios, Angelos 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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Identification Number: 10.1007/s00780-016-0302-6

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
Sets: Departments > Statistics
Collections > Economists Online
Date Deposited: 13 Jan 2016 14:30
Last Modified: 20 Jul 2019 02:11
URI: http://eprints.lse.ac.uk/id/eprint/64959

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