Revista Matemática Iberoamericana
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Published online: 2001-04-30
On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian optionsCatherine Donati-Martin, Raouf Ghomrasni and Marc Yor (1) Université Paris VI et VII, France
(2) Université Paris VI et VII, Paris, France
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.
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Donati-Martin Catherine, Ghomrasni Raouf, Yor Marc: On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options. Rev. Mat. Iberoamericana 17 (2001), 179-193. doi: 10.4171/RMI/292