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Brownian excursions and Parisian barrier options: a note

  • Michael Schröder (a1)

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.

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Postal address: Keplerstrasse 30, D-69469 Weinheim (Bergstrasse), Germany. Email address: schroeder@math.uni-mannheim.de

References

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[1] Chesney, M., Jeanblanc-Picqué, M., and Yor, M. (1997). Brownian excursions and Parisian barrier options. Adv. Appl. Prob. 29, 165184.
[2] Chesney, M. et al. (1997). Parisian barrier options—-a discussion. Risk, January 1997, 77—79.
[3] Doetsch, G. (1971). Handbuch der Laplace-Transformation, Band I, Theorie der Laplace-Transformation. Birkhäuser, Basel.
[4] Harrison, J. M. (1990). Brownian Motion and Stochastic Flow Systems. Krieger, Malabar, FL.
[5] Karatzas, I., and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus (Graduate Texts Math. 113), 2nd edn. Springer, New York.
[6] Lebedev, N. N. (1972). Special Functions and Their Applications. Dover, New York.
[7] Revuz, D., and Yor, M. (1994). Continuous Martingales and Brownian Motion, 2nd edn. Springer, Berlin.
[8] Schröder, M. (1999). On the valuation of Paris options: the first standard case. Preprint, Fakultät für Mathematik und Informatik, Universität Mannheim.
[9] Schröder, M. (2000). On the valuation of Paris options: the second standard case. Preprint, Fakultät für Mathematik und Informatik, Universität Mannheim.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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