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

Angelos Dassios and You You Zhang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Parisian options; excursion time; three state semi-Markov model; Laplace transform (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2016-06-02
New Economics Papers: this item is included in nep-dcm
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Citations: View citations in EconPapers (4)

Published in Finance and Stochastics, 2, June, 2016, 20, pp. 773-804. ISSN: 0949-2984

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