Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay

Abstract

The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler–Maruyama (EM) method to study properties of the numerical solutions under the local Lipschitz condition plus Khasminskii-type condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds.