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Abstract

Observing that the recent developments of spatial discretization schemes based on recursive (product) quantization can be applied to a wide family of discrete time Markov chains, including all standard time discretization schemes of diffusion processes, we establish in this paper a generic strong error bound for such quantized schemes under a Lipschitz propagation assumption. We also establish a marginal weak error estimate that is entirely new to our best knowledge. As an illustration of their generality, we show how to recursively quantize the Euler scheme of a jump diffusion process, including details on the algorithmic aspects grid computation, transition weight computation, etc. Finally, we test the performances of the recursive quantization algorithm by pricing a European put option in a jump Merton model.

recursive quantization, weak error analysis, strong error analysis, jump diffusion, pricing jump model
© The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://dbpia.nl.go.kr/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
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