IJAM, Volume 27, No. 4 (2014)

Abstract. Vasicek [14] was the first to propose a three constant-parameter one-factor short rate model for the evolution of interest rates and it was the first model to incorporate mean reversion, an essential characteristic of interest rates. We consider a generalization of Vasicek model in which the normal level of the short rate is an exponentially weighted average of past short rates as suggested in the work of Malkiel [12]. The differential equation giving the price of a zero-coupon bond by this generalized Vasicek-Malkiel model is derived. A complete explicit solution is then obtained as well as the yield curve. We then consider a further extension of the generalized Vasicek-Malkiel model by letting one of the parameters to be time dependent and utilize it to incorporate today's term structure of interest rates into the model and, again, an explicit solution is obtained.