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Double-Barrier Parisian Options

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Angelos Dassios  and
Shanle Wu
Angelos Dassios*
Affiliation:
London School of Economics
Shanle Wu*
Affiliation:
London School of Economics
*
∗Postal address: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK.
∗Postal address: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK.
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Abstract

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In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

Keywords

Excursion timefour-state semi-Markov modeldouble-barrier Parisian optionLaplace transform

MSC classification

Secondary: 60J65: Brownian motion 60G44: Martingales with continuous parameter 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 1 - 20
Copyright
Copyright © Applied Probability Trust 2011 

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