BIROn - Birkbeck Institutional Research Online

Functionals of exponential Brownian motion and divided differences

Baxter, Brad J.C. and Brummelhuis, Raymond (2011) Functionals of exponential Brownian motion and divided differences. Journal of Computational and Applied Mathematics 236 (4), pp. 424-433. ISSN 0377-0427.

[img]
Preview
Text (Post-print (Refereed))
3050.pdf

Download (407Kb) | Preview
Official URL: http://dx.doi.org/10.1016/j.cam.2011.06.010

Abstract

We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and its time average, and we find the use of divided differences greatly elucidates formulae, providing a path to several new results. As applications, we find that this correlation coefficient is always at least 1/p2 and, via the Hermite–Genocchi integral relation, demonstrate that all moments of the time average are certain divided differences of the exponential function. We also prove that these moments agree with the somewhat more complex formulae obtained by Oshanin and Yor.

Item Type: Article
Keyword(s) / Subject(s): Brownian motion, moments, divided differences, Asian options
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Administrator
Date Deposited: 08 Feb 2011 14:34
Last Modified: 30 Aug 2013 09:27
URI: http://eprints.bbk.ac.uk/id/eprint/3050

Archive Staff Only (login required)

Edit/View Item Edit/View Item