The Distribution of the Quantile of a Brownian Motion with Drift and the Pricing of Related Path-Dependent Options

Authors
Dassios, Angelos
Citation
Dassios, Angelos, The Distribution of the Quantile of a Brownian Motion with Drift and the Pricing of Related Path-Dependent Options, Annals of applied probability , 5(2), 1995, pp. 389-398
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
5
Issue
2
Year of publication
1995
Pages
389 - 398
Database
ACNP
SICI code
Abstract
The study of the quantile of a Brownian motion with a drift is undertaken. An explicit formula for its density, as well as a representation of its distribution as the sum of the maximum and the minimum of two rescaled independent Brownian motions with drift, is given. The result is used in the pricing of a financial path-dependent option due to Miura.