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

Angelos Dassios () and You You Zhang
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Angelos Dassios: London School of Economics
You You Zhang: London School of Economics

Finance and Stochastics, 2016, vol. 20, issue 3, No 7, 773-804

Abstract: 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; 91B25; 60K15; 60J27; 60J65 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-016-0302-6

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