  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.
