The family of the Affine Term Structure of interest rate has been a lot
developed in the literature since the first work of Vasicek (1977) and Cox, Ingersoll and
Ross (1985b). Although their performances increase, they are still facing several difficulties
in their capacity to fully explain the behaviour of the Term Structure of interest rate. Some
of these issues are explain by the omission of non linear relation in the affine model (Dai
and Singleton, 1999). This paper is in the continuity of this reflexion. It presents, develops,
applies and discuses the quadratic model defined by Realdon (2006).