A Semi-Markov Modulated Interest Rate Model

TL;DR

This paper introduces a semi-Markov modulated interest rate model combining a semi-Markov switching process with a diffusive process, providing recursive moment equations and a Monte Carlo simulation method, extending classical models.

Contribution

It develops a novel semi-Markov modulated interest rate model with recursive moment calculations and simulation algorithms, enhancing classical models like Vasicek and CIR.

Findings

Derived recursive equations for higher order moments.

Developed a Monte Carlo simulation algorithm.

Extended classical interest rate models with semi-Markov modulation.

Abstract

In this paper we propose a semi-Markov modulated model of interest rates. We assume that the switching process is a semi-Markov process with finite state space E and the modulated process is a diffusive process. We derive recursive equations for the higher order moments of the discount factor and we describe a Monte Carlo al- gorithm to execute simulations. The results are specialized to classical models as those by Vasicek, Hull and White and CIR with a semi-Markov modulation.