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    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.

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    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: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Administrator
    Date Deposited: 08 Feb 2011 14:34
    Last Modified: 09 Aug 2023 12:30


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