The joint distribution of Parisian and hitting times of Brownian motion with application to Parisian option pricing |
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Authors: | Angelos Dassios You You Zhang |
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Affiliation: | 1.Department of Statistics,London School of Economics,London,UK |
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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. |
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