The initial formulation of Vasicek’s model is very general, with the short-term interest rate being described by a diffusion process. An arbitrage argument, similar to that used to derive the Black-Scholes option pricing formula, is applied within this broad framework to determine the partial differential equation satisfied by any contingent claim. A stochastic representation of the bond price results from the solution to this equation. Vasicek then allows more restrictive assumptions to formulate the specific model with which his name is associated.

The consistency of the model specifications with an underlying economic equilibrium is not proved. Rather, it is implicitly assumed. The special case of the general model formulation, which Vasicek uses for illustrative purposes, was suggested by Merton [40] in a study of price dynamics in a continuous time, equilibrium economy. Equilibrium conditions imply that interest rates are such that the demand and supply of capital are equally matched.

Few of the early studies of asset prices within an equilibrium economy setting were applicable to interest rates, mainly focusing on stock prices. If we accept Vasicek’s implicit assumption that the functional form of the short-term interest rate process and market price of risk are in fact consistent with an economic equilibrium, then his work may be seen as a complete characterisation of the interest rate term structure in such an economy. This simple model has been praised for its incorporation of reversion to a long-run mean and the ability to produce an analytic representation of discount bond prices. On the other hand, it has been criticised for allowing interest rates to become negative and not providing a mechanism by which the initial, market-observed term structure may be reproduced.