Analytical valuation of American-style Asian options

This article derives the first analytical pricing formulas for American-sty le Asian options of the so-called floating strike type. Geometric as well a s arithmetic averaging Is considered. The setup is a standard Black-Scholes framework where the price of the underlying security evolves according to a geometric Brownian motion. A decomposition result that splits up the valu e of the floating strike American option into the price of an otherwise equ ivalent European option and an early exercise premium is first presented. T his decomposition result is then manipulated further for the two separate t ypes of averaging. With geometric averaging we derive an exact pricing form ula, whereas with arithmetic averaging we develop an analytical approximati on formula that proves to be very precise. Numerical examples are provided.