Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation

Deng, Shounian and Fei, Chen and Fei, Weiyin and Mao, Xuerong (2019) Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation. Physica A: Statistical Mechanics and its Applications, 533. 122057. ISSN 0378-4371

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    Abstract

    In this paper, we consider a generalized Ait-Sahalia interest rate model with Poisson jumps in finance. The analytical properties including positivity, boundedness and pathwise asymptotic estimations of the solution to this model are investigated. Moreover, we prove that the EulerMaruyama (EM) numerical solution converges to the true solution of the model in probability. Finally, we apply the EM solution to compute some financial quantities. A numerical example is provided to demonstrate the effectiveness of our results.