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

Authors
Donati-Martin, C Ghomrasni, R Yor, M
Citation
C. Donati-martin et al., On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options, REV MAT IBE, 17(1), 2001, pp. 179-193
Citations number
22
Categorie Soggetti
Mathematics
Journal title
REVISTA MATEMATICA IBEROAMERICANA
ISSN journal
02132230 → ACNP
Volume
17
Issue
1
Year of publication
2001
Pages
179 - 193
Database
ISI
SICI code
0213-2230(2001)17:1<179:OCMPAT>2.0.ZU;2-R
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, t] of a geometric Brownian motion and the value at time t of a Markov process, for which we can compute explicitly the resolvent.