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

Abstract

In this paper, we consider the generalized Ait-Sahaliz interest rate model with Poisson jumps in finance. The analytical properties including the positivity, boundedness and pathwise asymptotic estimations of the solution to the model are investigated. Moreover, we prove that the Euler-Maruyama (EM) numerical solutions will converge to the true solution in probability. Finally, under assumption that the interest rate or the asset price is governed by this model, we apply the EM solutions to compute some financial quantities.

References in corpus (2)

• Testing for jumps in a discretely observed process
• Estimating the degree of activity of jumps in high frequency data

Cited by in corpus (3)

• Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure
• First order strong approximation of Ait-Sahalia-type interest rate model with Poisson jumps
• Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations