A dynamic programming procedure for pricing American-style Asian options

Pricing European-style Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no easily computable analytical solution is available. Pricing their American-style counterparts, which provide early exercise opportunities, poses the additional difficulty of solving a dynamic optimization problem to determine the optimal exercise strategy. A procedure for pricing American-style Asian options of the Bermudan flavor, based on dynamic programming combined with finite-element piecewise-polynomial approximation of the value function, is developed here. A convergence proof is provided. Numerical experiments illustrate the consistency and efficiency of the procedure. Theoretical properties of the value function and of the optimal exercise strategy are also established.