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Recursive formula for the double-barrier Parisian stopping time

Part of: Probabilistic methods, simulation and stochastic differential equations Mathematical finance Markov processes

Published online by Cambridge University Press:  28 March 2018

Angelos Dassios  and
Jia Wei Lim
Angelos Dassios*
Affiliation:
London School of Economics and Political Science
Jia Wei Lim*
Affiliation:
University of Bristol
*
* Postal address: Department of Statistics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK. Email address: [email protected]
** Postal address: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK. Email address: [email protected]
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Abstract

In this paper we obtain a recursive formula for the density of the double-barrier Parisian stopping time. We present a probabilistic proof of the formula for the first few steps of the recursion, and then a formal proof using explicit Laplace inversions. These results provide an efficient computational method for pricing double-barrier Parisian options.

Keywords

Brownian excursionParisian stopping timedouble-sided Parisian option

MSC classification

Primary: 65C50: Other computational problems in probability
Secondary: 60J65: Brownian motion 91G60: Numerical methods (including Monte Carlo methods)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 282 - 301
Copyright
Copyright © Applied Probability Trust 2018 

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References

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