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

Autores: Marc Yor, R. Ghomrasni, C. Donati-Martin
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 17, Nº 1, 2001, págs. 179-193
Idioma: inglés
DOI: 10.4171/rmi/292
Títulos paralelos:
- Procesos de Markov ligados a funcionales exponenciales del movimiento browniano: aplicación a las opciones asiáticas.
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Resumen
- 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.