IJAM: Volume 29, No. 1 (2016)

Abstract. A four-parameter random walk model for the short rate of interest is described in Wilmott et al. [15]. For pricing zero-coupon bonds from the resulting partial differential equation based on this short rate model, a certain form of solution requires the solution of two first-order nonlinear ordinary differential equations. In the present paper we show the interesting result that, for obtaining solutions of the bond pricing equation, neither of these two equations requires any differential equation solving techniques; in fact, both these first-order nonlinear differential equations can be solved simply by elementary integration. We include the corresponding yield curve and its asymptotic behavior. We identify our results obtained here for the general four-parameter model in the two special cases of Vasicek [14] and Cox, Ingersoll and Ross [4] with those given by these authors.