Markov switching quadratic term structure models

TL;DR

This paper introduces a regime switching quadratic term structure model for interest rates, capturing different economic states with a Markov process, and derives explicit formulas for bond prices and stochastic coefficients.

Contribution

It develops a novel regime switching quadratic term structure model with explicit recursive formulas for bond prices and stochastic coefficients.

Findings

Conditional zero coupon bond prices have a quadratic structure.

Stochastic coefficients satisfy explicit coupled backward recursions.

Model captures different economic regimes effectively.

Abstract

In this paper, we consider a discrete time economy where we assume that the short term interest rate follows a quadratic term structure of a regime switching asset process. The possible non-linear structure and the fact that the interest rate can have different economic or financial trends justify the interest of Regime Switching Quadratic Term Structure Model (RS-QTSM). Indeed, this regime switching process depends on the values of a Markov chain with a time dependent transition probability matrix which can well captures the different states (regimes) of the economy. We prove that under this modelling that the conditional zero coupon bond price admits also a quadratic term structure. Moreover, the stochastic coefficients which appear in this decomposition satisfy an explicit system of coupled stochastic backward recursions.