Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On certain Markov processes attached to exponential functionals of Brownian motion ; application to Asian options.

Auteur(s):

Code(s) de Classification MSC:

Résumé: We obtain a closed formula for the Laplace transform of the first moment of certain exponential functionals of Brownian motion with drift, which gives the price of Asian options. The proof relies on an identity in law between the average on $[0,t]$ of a geometric Brownian motion and the value at time $t$ of a Markov process, for which we can compute explicitly the resolvent.

Mots Clés: exponentials of Brownian motion; Asian options; generalized Ornstein-Uhlenbeck processes

Date: 1999-03-26

Prépublication numéro: PMA-495