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

Author

Listed:
  • Deng, Shounian
  • Fei, Chen
  • Fei, Weiyin
  • Mao, Xuerong

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 Euler–Maruyama (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.

Suggested Citation

  • Deng, Shounian & Fei, Chen & Fei, Weiyin & 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, Elsevier, vol. 533(C).
    • Handle: RePEc:eee:phsmap:v:533:y:2019:i:c:s0378437119312014
    DOI: 10.1016/j.physa.2019.122057
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    Citations

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    Cited by:

    1. Przybyłowicz, Paweł & Szölgyenyi, Michaela, 2021. "Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Lord, Gabriel & Wang, Mengchao, 2024. "Convergence of a exponential tamed method for a general interest rate model," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    3. Emmanuel Coffie, 2021. "Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations," Papers 2103.07651, arXiv.org, revised Jul 2021.

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