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Reports (Research Report) Year : 2002

First order schemes in the numerical quantization method

Vlad Bally
  • Function : Author
Gilles Pagès
  • Function : Author
  • PersonId : 856726
  • IdHAL : gilpag
Jacques Printems
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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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Dates and versions

inria-00072164 , version 1 (23-05-2006)


  • 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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