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First order schemes in the numerical quantization method

Vlad Bally 1 Gilles Pagès Jacques Printems
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : The numerical quantization method (see [B.P.1, B.P.2, B.P.P.1]) is a grid method which relies on the approximation of the solution of a nonlinear problem (e.g. backward Kolmogorov equation) by piecewise constant functions. Its purpose is to compute a large number of conditional expectations along the path of the associated diffusion process. We give here an improvement of this method by describing a first order scheme based on piecewise linear approximations. Main ingredients are correction terms in the transition probabilities weights. We emphasize the fact that in the case of optimal quantization, a non neglectable number of correction terms vanish. We think that this is a strong argument to use it. The problem of pricing and hedging American options is investigated and a priori estimates of the errors are established.
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Submitted on : Tuesday, May 23, 2006 - 7:57:00 PM
Last modification on : Friday, February 4, 2022 - 3:12:55 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:56:27 PM


  • HAL Id : inria-00072164, version 1



Vlad Bally, Gilles Pagès, Jacques Printems. First order schemes in the numerical quantization method. [Research Report] RR-4424, INRIA. 2002. ⟨inria-00072164⟩



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