Abstract
This paper derives analytical pricing formulas for American-style Asian options. Geometric as well as 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 value of the floating strike American-style Asian option into the price of an otherwise equivalent European option and an early exercise premium is first presented. This decomposition result is then manipulated further for the two separate types of averaging. With geometric averaging we derive an exact pricing formula which is easily implemented whereas with arithmetic averaging we develop a similar analytical approximation formula which proves to be very accurate. Numerical results are provided.
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