Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

A quantization tree method for pricing and hedging multi-dimensional American options


Code(s) de Classification MSC:

Résumé: 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 grid designed to minimize the (square mean) projection error ([22]). An algorithm to compute such grids is described. We provide results concerning the orders of the approximation with respect to the regularity of the pay-off function and the global size of the grids. Numerical tests are performed in dimensions $2$, $4$, $6$, $10$ with American style exchange options. They show that theoretical orders are probably pessimistic.

Mots Clés: American option pricing ; Optimal Stopping ; Snell envelope ; quantization of random vectors

Date: 2002-08-30

Prépublication numéro: PMA-753

Pdf file : PMA-753.pdf