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The present article provides an efficient and accurate hybrid method to priceAmerican standard options in certain jump-diffusion models as well as Americanbarrier-type options under the Black & Scholes framework. Our methodgeneralizes the quadratic approximation scheme of Barone-Adesi & Whaley (1987)and several of its extensions. Using perturbative arguments, we decompose theearly exercise pricing problem into sub-problems of different orders and solvethese sub-problems successively. The obtained solutions are combined to recoverapproximations to the original pricing problem of multiple orders, with the0-th order version matching the general Barone-Adesi & Whaley ansatz. We testthe accuracy and efficiency of the approximations via numerical simulations.The results show a clear dominance of higher order approximations over theirrespective 0-th order version and reveal that significantly more pricingaccuracy can be obtained by relying on approximations of the first few orders.Additionally, they suggest that increasing the order of any approximation byone generally refines the pricing precision, however that this happens at theexpense of greater computational costs.

On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options