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 nonlinear structure and the fact that the interest rate can have different economic or financial trends justify regime-switching quadratic term structure model. 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.