Pricing American-Style Derivatives with European Call Options

Authors:
Scott B. Laprise;Michael C. Fu;Steven I. Marcus;Andrew E. B. Lim;Huiju Zhang
Affiliations:
BAE Systems, Advanced Information Technologies, 3811 N. Fairfax Drive, Arlington, Virginia 22203;The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742;Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742;Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720;The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742
Venue:
Management Science
Year:
2006

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Abstract

We present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call-option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to the pricing of a portfolio of European call options, leading to analytical expressions for those cases where analytical European call prices are available (e.g., the Merton jump-diffusion process). Furthermore, in many settings, the approach yields upper and lower analytical bounds that provably converge to the true option price. We provide computational results to illustrate the convergence and accuracy of the resulting estimators.