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

TL;DR

This paper studies a generalized interest rate model with Poisson jumps, analyzing its properties and proving the convergence of Euler-Maruyama numerical solutions, with applications to financial quantity computations.

Contribution

It introduces a generalized Ait-Sahalia-type model with jumps, investigates its key properties, and proves the convergence of numerical solutions in a financial context.

Findings

Positivity and boundedness of solutions established

Euler-Maruyama solutions converge in probability

Numerical methods applied to compute financial quantities

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.