Abstract
This paper pursues the role of Laguerre series in the explicit valuation of contingent claims in general and Asian options in particular. Motivated by Dufresne (2000), we study how they permit one to reduce these questions to computing moments. Two alternative such Laguerre reduction approaches are proposed and analyzed. Sufficient conditions for their validity are developed as a further novel feature; these are in terms of local growth measures for the payoff functions and the densities that the paper introduces for this purpose. Our methods are exemplified by considering the benchmark valuation of Asian options. Our explicit formulas for the negative moments of the integral of geometric Brownian motion in terms of theta functions are instrumental here. They have been derived in Schröder (2003c) building on work of Dufresne (2000), and this paper now finally develops their pertinent computational aspects.
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