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The Central Limit Theorem for a non linear algorithm based on quantization

Vlad Bally 1 
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : In a serry of papers we have presented an algorithm based on quantization for pricing American options. More generally this amounts to solve numerically an obstacle problem for some semi linear PDE^s. Our algorithm is based on a Monte Carlo method and so a statistical error comes on. In the present paper we study this error: we prove the Central Limit Theorem for the algorithm and we give evaluations of the variance.. The difficulty comes from the fact that the algorithm is not linear. On the other hand an interesting problem is to control the behaviour of the variance of the algorithm as the complexity increases.. It turns out that the variance does not blow up if the time discretization step and the space discretization step tend to zero
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Reports (Research report)
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Submitted on : Tuesday, May 23, 2006 - 7:21:23 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:29 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:30:45 PM


  • HAL Id : inria-00071956, version 1



Vlad Bally. The Central Limit Theorem for a non linear algorithm based on quantization. [Research Report] RR-4629, INRIA. 2002. ⟨inria-00071956⟩



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