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On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps (2002.09203v2)
Published 21 Feb 2020 in math.NA and cs.NA
Abstract: This article aims to reveal the mean-square convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahaliz interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves positivity of the original problem. Furthermore, we successfully recover the mean-square convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.