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

TL;DR

This paper introduces a modified hybrid Poisson-jump Ait-Sahalia interest rate model with delay, addressing empirical phenomena like volatility skews, jumps, and crises, and develops numerical approximation methods for its analysis.

Contribution

It proposes a new hybrid interest rate model incorporating jumps and delays, and develops truncated EM techniques for its numerical approximation and payoff computation.

Findings

Model better captures empirical interest rate phenomena

Developed truncated EM methods for model approximation

Validated methods within Monte Carlo simulations

Abstract

While the original Ait-Sahalia interest rate model has been found considerable use as a model for describing time series evolution of interest rates, it may not possess adequate specifications to explain responses of interest rates to empirical phenomena such as volatility 'skews' and 'smiles', jump behaviour, market regulatory lapses, economic crisis, financial clashes, political instability, among others collectively. The aim of this paper is to propose a modified version of this model by incorporating additional features to collectively describe these empirical phenomena adequately. Moreover, due to lack of a closed-form solution to the proposed model, we employ several new truncated EM techniques to examine this model and justify the scheme within Monte Carlo framework to compute expected payoffs of some financial quantities such as a bond and a barrier option.