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We provide a surprising new application of classical approximation theory toa fundamental asset-pricing model of mathematical finance. Specifically, wecalculate an analytic value for the correlation coefficient between exponentialBrownian motion and its time average, and we find the use of divideddifferences greatly elucidates formulae, providing a path to several newresults. As applications, we find that this correlation coefficient is alwaysat least $1/\sqrt{2}$ and, via the Hermite--Genocchi integral relation,demonstrate that all moments of the time average are certain divideddifferences of the exponential function. We also prove that these moments agreewith the somewhat more complex formulae obtained by Oshanin and Yor.

Functionals of Exponential Brownian Motion and Divided Differences