First order strong approximation of Ait-Sahalia-type interest rate model with Poisson jumps

2021/10/29 by Ziyi Lei, Lei, Ziyi, Siqing Gan +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Differential Equations and Numerical Methods #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2110.15482

Abstract

For Ait-Sahalia-type interest rate model with Poisson jumps, we are interested in strong convergence of a novel time-stepping method, called transformed jump-adapted backward Euler method (TJABEM). Under certain hypothesis, the considered model takes values in positive domain (0,∞). It is shown that the TJABEM can preserve the domain of the underlying problem. Furthermore, for the above model with non-globally Lipschitz drift and diffusion coefficients, the strong convergence rate of order one of the TJABEM is recovered with respect to a L^p-error criterion. Finally, numerical experiments are given to illustrate the theoretical results.

Citations

• Numerical methods for nonlinear stochastic differential equations with jumps

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