A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS |
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Authors: | Vlad Bally Gilles Pagès Jacques Printems |
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Institution: | Laboratoire d'analyse et de mathématiques appliquées (CNRS UMR 8050) &Projet MathFi (INRIA), Universitéde Marne-la-Vallée, France; Laboratoire de Probabilités et Modèles aléatoires, (CNRS UMR 7599) UniversitéParis 6; Centre de Mathématiques, (CNRS UMR 8050) UniversitéParis 12, Créteil |
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Abstract: | We present here the quantization method which is well-adapted for the pricing and hedging of American options on a basket of assets. Its purpose is to compute a large number of conditional expectations by projection of the diffusion on optimal grids designed to minimize the (square mean) projection error ( Graf and Luschgy 2000 ). An algorithm to compute such grids is described. We provide results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids. Numerical tests are performed in dimensions 2, 4, 5, 6, 10 with American style exchange options. They show that theoretical orders are probably pessimistic. |
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Keywords: | American option pricing optimal stopping Snell envelope optimal quantization local volatility model |
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