Exponential Brownian motion and divided differences

We calculate an analytic value for the correlation coefficient between a geometric, or exponential, Brownian motion and its time-average, a novelty being our use of divided differences to elucidate formulae. This provides a simple approximation for the value of certain Asian options regarding them as exchange options. We also illustrate that the higher moments of the time-average can be expressed neatly as divided differences of the exponential function via the Hermite-Genocchi integral relation, as well as demonstrating that these expressions agree with those obtained by Oshanin and Yor when the drift term vanishes.