A regime switching model to evaluate bonds in a quadratic term structure of interest rates

In this article, we consider a discrete time economy in which we assume that the short term interest rate follows a quadratic term structure in 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 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 capture the different states (regimes) of the economy. We prove that under this model, the conditional zero coupon bond price admits a quadratic term structure. Moreover, the stochastic coefficients which appear in this decomposition satisfy an explicit system of coupled stochastic backward recursions.