• V. BALLY
• G. PAGÈS
• J. PRINTEMS

Code(s) de Classification MSC:

• 90A09 Finance, portfolios, investment
• 60G40 Stopping times; optimal stopping problems; gambling theory, See also {62L15, 90D60}
• 65C05 Monte Carlo methods
• 65C20 Models, numerical methods
• 93E23 Stochastic gradient methods
• 65N50 Mesh generation and refinement

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