IJAM, Volume 28, No. 1 (2015)

Abstract. We consider a four-parameter short rate model for the evolution of interest rates. In this model we take \textit{normal level} of the short rate as an exponentially weighted average of the past short rates as suggested by Malkiel [14]. We first derive the differential equation for the price of a zero-coupon bond under this model. A complete explicit solution of the partial differential equation is obtained under a suitable simplifying assumption to obtain an explicit model for the evolution of interest rates. The relevant yield curve is also obtained. We then consider a most desirable feature of an interest rates model, incorporating current term structure of interest rates into the model. Again, a complete explicit solution is obtained together with the yield curve and its asymptotic behaviour. A well-known previously given model is included and discussed in the context of our present interest rates model.