An interest rate model with a Markovian mean reverting level

Abstract

A two‐factor Vasicek model, where the mean reversion level changes according to a continuous time finite state Markov chain, is considered. This model could capture the behaviour of monetary authorities who normally set a reference rate which changes from time to time. We derive the term structure via the analytic expression of the bond price that involves a fundamental matrix. The validity of the bond price closed form solution is verified via the forward rate dynamics.