Pricing calibrated American options by stochastic linear programming Fabio Antonelli * Carlo Mancini † Mustafa C ¸ . Pınar ‡ October 31, 2012 Abstract We propose an approach for computing the arbitrage-free interval of an American option in discrete incomplete market models via lin- ear programming. The main idea is to look for strategies that use both the basic asset and some European derivatives available on the market for trading. This method goes under the name of calibrated option pricing and it has given significant results for European op- tions. Here we extend the analysis to American options showing that for the arbitrage-free interval can be characterized in terms of mar- tingale measures and that it gets reduced significantly with respect to the non calibrated case. 1 Introduction In this work we apply a linear programming method to price American op- tions in a discrete and incomplete market model. The linear programming theory has been used in contexts of completeness by Naik (ref. [8]), Ortu * University of L’Aquila, Italy † University of L’Aquila, Italy ‡ Bilkent University, Turkey. 1