Laguerre series for Asian and other options (Q2707158)

This paper has following 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; and 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.