The Annals of Applied Probability

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

Angelos Dassios

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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.

Article information

Source
Ann. Appl. Probab., Volume 5, Number 2 (1995), 389-398.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004770

Digital Object Identifier
doi:10.1214/aoap/1177004770

Mathematical Reviews number (MathSciNet)
MR1336875

Zentralblatt MATH identifier
0837.60076

JSTOR
links.jstor.org

Subjects
Primary: 60J65: Brownian motion [See also 58J65]

Keywords
Quantiles of Brownian motion with a drift Feyman-Kac occupation time path-dependent financial options

Citation

Dassios, Angelos. The Distribution of the Quantile of a Brownian Motion with Drift and the Pricing of Related Path-Dependent Options. Ann. Appl. Probab. 5 (1995), no. 2, 389--398. doi:10.1214/aoap/1177004770. https://projecteuclid.org/euclid.aoap/1177004770


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