Title: Accuracy measures for American put option pricing algorithms

Authors: David H. Goldenberg

Addresses: Lally School of Management and Technology, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

Abstract: I address the dichotomy between American put option pricing theory and the numerical algorithms designed to estimate American put option prices. The literature has focused only on pricing error. However, early exercise is the essence of American option pricing (exercising) and with it comes the possibility of early exercise error and its opportunity costs. I introduce an economically viable metric that identifies all the errors of American put option pricing algorithms. The accuracy of such algorithms can thereby be fully assessed. A rational option pricing result generalises the usual integral equation and motivates pure pricing error. This provides new intuition for the optimality condition for early exercise. Early exercise error is motivated by comparing discounted expected profits generated by the estimated model vs. the optimal early exercise model. The error measure applies to any put pricing algorithm and any benchmark. We illustrate our total error measure with a new algorithm.

Keywords: accuracy measures; American put options; derivatives; early exercise boundaries; early exercise error; integral equation; put pricing algorithms; multiply iterated binomial; option pricing.

DOI: 10.1504/IJFMD.2009.028942

International Journal of Financial Markets and Derivatives, 2009 Vol.1 No.1, pp.5 - 40

Published online: 14 Oct 2009 *

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