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First-Order Schemes in the Numerical Quantization Method (2003)

Bally, V. ; Pagès, G. ; Printems, J.

350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.

Mathematical finance 13 (2003), S. 0

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ISSN: 1467-9965

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Mathematics , Economics

Notes: The numerical quantization method is a grid method that relies on the approximation of the solution to a nonlinear problem 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 probability weights. We emphasize the fact that in the case of optimal quantization, many of these correcting 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 proposed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/1467-9965.t01-1-00002

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