Numerical approximation of a hybrid Poisson-jump Ait-Sahalia-type interest rate model with delay

While the original Ait-Sahalia interest rate model has been found to be of considerable use for describing the time-series evolution of interest rates, it may not possess adequate specifications to explain the responses of interest rates to empirical phenomena such as volatility skew-smile effect, jumps, market regulatory lapses, economic crises, financial clashes, and political instability, among others collectively. In this article, we propose a modified version of this model by incorporating additional features to help collectively describe these empirical phenomena adequately. Since the proposed model does not have a closed-form formula, we construct new techniques of the truncated EM method to study it and justify the method within a Monte Carlo framework to compute some financial quantities.