JournalsrmiVol. 17, No. 1pp. 179–193

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

  • Catherine Donati-Martin

    Université Paris VI et VII, France
  • Raouf Ghomrasni

    Université Paris VI et VII, Paris, France
  • Marc Yor

    Université Paris VI, France
On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options cover
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Abstract

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,tt] of a geometric Brownian motion and the value at time tt of a Markov process for which we can compute explicitly the resolvent.

Cite this article

Catherine Donati-Martin, Raouf Ghomrasni, Marc Yor, On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options. Rev. Mat. Iberoam. 17 (2001), no. 1, pp. 179–193

DOI 10.4171/RMI/292