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

DOI10.1007/S11075-022-01494-6arXiv2110.15482OpenAlexW4316805144MaRDI QIDQ6133889

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Publication date: 21 August 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

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 $(0,infty)$. 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.

Full work available at URL: https://arxiv.org/abs/2110.15482

zbMATH Keywords

Poisson jumpsstrong convergence rateAit-Sahalia-type interest rate modeltransformed jump-adapted backward Euler method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical analysis (65-XX)

Related Items (3)

Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation ⋮ Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model ⋮ On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps

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