The Vasicek Model

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 [8], 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.