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Brownian excursions and Parisian barrier options: a note

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Michael Schröder
Michael Schröder*
Affiliation:
Universität Mannheim
*
∗Postal address: Keplerstrasse 30, D-69469 Weinheim (Bergstrasse), Germany. Email address: [email protected]
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Abstract

This paper addresses Paris barrier options, as introduced by G. Kentwell and J. Cornwall at Bankers Trust Australia in the mid-1990s, and their valuation, as developed by Chesnay, Jeanblanc-Picqué and Yor using the Laplace-transform approach. The notion of Paris barrier options is extended so that their valuation becomes possible at any point during their lifespan, and the pertinent Laplace transforms of Chesnay, Jeanblanc-Picqué and Yor are modified when necessary.

Keywords

Brownian excursionsBrownian meanderbarrier optionsLaplace transform

MSC classification

Primary: 60G46: Martingales and classical analysis
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 855 - 864
Copyright
Copyright © Applied Probability Trust 2003 

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References

Chesney, M., Jeanblanc-Picqué, M., and Yor, M. (1997). Brownian excursions and Parisian barrier options. Adv. Appl. Prob. 29, 165–184.CrossRefGoogle Scholar
Chesney, M. et al. (1997). Parisian barrier options—-a discussion. Risk, January 1997, 77—79.Google Scholar
Doetsch, G. (1971). Handbuch der Laplace-Transformation, Band I, Theorie der Laplace-Transformation. Birkhäuser, Basel.Google Scholar
Harrison, J. M. (1990). Brownian Motion and Stochastic Flow Systems. Krieger, Malabar, FL.Google Scholar
Karatzas, I., and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus (Graduate Texts Math. 113), 2nd edn. Springer, New York.Google Scholar
Lebedev, N. N. (1972). Special Functions and Their Applications. Dover, New York.Google Scholar
Revuz, D., and Yor, M. (1994). Continuous Martingales and Brownian Motion, 2nd edn. Springer, Berlin.Google Scholar
Schröder, M. (1999). On the valuation of Paris options: the first standard case. Preprint, Fakultät für Mathematik und Informatik, Universität Mannheim.Google Scholar
Schröder, M. (2000). On the valuation of Paris options: the second standard case. Preprint, Fakultät für Mathematik und Informatik, Universität Mannheim.Google Scholar