On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps
Numerical Analysis
2020-08-14 v2 Numerical Analysis
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.
Cite
@article{arxiv.2002.09203,
title = {On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps},
author = {Yuying Zhao and Xiaojie Wang and Mengchao Wang},
journal= {arXiv preprint arXiv:2002.09203},
year = {2020}
}