Another look at the integral of exponential Brownian motion and the pricing of Asian options

Andrew Lyasoff ()
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Andrew Lyasoff: Boston University

Finance and Stochastics, 2016, vol. 20, issue 4, No 8, 1096 pages

Abstract: Abstract It is shown that Marc Yor’s formula (Adv. Appl. Probab. 24:509–531, 1992) for the density of the integral of exponential Brownian motion taken over a finite time interval is an extremal member of a family of previously unknown integral formulae for the same density. The derivation is independent from the one by Yor and obtained from a simple time-reversibility feature, in conjunction with a Fokker–Planck type argument. Similar arguments lead to an independent derivation of Dufresne’s result (Scand. Actuar. J. 90:39–79, 1990) for the law of the integral taken over an infinite time interval. The numerical aspects of the new formulae are developed, with concrete applications to Asian options.

Keywords: Exponential Brownian motion; Random environment; Asian options; 60J65; 60J60 (search for similar items in EconPapers)
JEL-codes: C63 C65 G13 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-016-0307-1

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