Laguerre Series for Asian and Other Options

This paper has four goals: (a) relate ladder height distributions to option values; (b) show how Laguerre expansions may be used in the computation of densities, distribution functions and option prices; (c) derive some new results on the integral of geometric Brownian motion over a finite interval; (d) apply the preceding results to the determination of the distribution of the integral of geometric Brownian motion and the computation of Asian option values. The usual fixed-strike options on the average are treated, as well as options with payoffs expressed in terms of one over the average of the underlying security, which this author calls “reciprocal Asian options.” In all cases the underlying asset is represented by geometric Brownian motion, the averages are performed continuously, and the options are of European type. Option pricing; Asian option; reciprocal Asian option; exponential functional of Brownian motion