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Pricing path-dependent options in a Black-Scholes market from the distribution of homogeneous Brownian functionals

Part of: Markov processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

T. Fujita ,
F. Petit  and
M. Yor
T. Fujita*
Affiliation:
Hitotsubashi University
F. Petit*
Affiliation:
Université Paris VI
M. Yor*
Affiliation:
Université Paris VI
*
∗ Postal address: Graduate School of Commerce and Management, Hitotsubashi University, Naka 2-1, Kunitachi, Tokyo, 186-8601, Japan. Email address: fujita@math.hit-u.ac.jp
∗∗ Postal address: Laboratoire de Probabilités, Université Paris VI, casier 188, 4, Place Jussieu, 75252 Paris Cedex 05, France.
∗∗ Postal address: Laboratoire de Probabilités, Université Paris VI, casier 188, 4, Place Jussieu, 75252 Paris Cedex 05, France.
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Abstract

We give some explicit formulae for the prices of two path-dependent options which combine Brownian averages and penalizations. Because these options are based on both the maximum and local time of Brownian motion, obtaining their prices necessitates some involved study of homogeneous Brownian functionals, which may be of interest in their own right.

Keywords

Brownian motionBrownian supremumBrownian local timeoptions with barriers and penalties

MSC classification

Primary: 60J55: Local time and additive functionals 60J65: Brownian motion 91B70: Stochastic models
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 1 - 18
Copyright
Copyright © Applied Probability Trust 2004 

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