Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation
Provides theoretical guarantees for a financial model, but the contribution is incremental as it extends existing Ait-Sahalia-type models with jumps and standard convergence results.
This paper studies a generalized interest rate model with Poisson jumps, proving positivity, boundedness, and pathwise asymptotic estimates, and shows that Euler-Maruyama numerical solutions converge in probability to the true solution.
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.