An Overview of the Vasicek Short Rate Model

Abstract

The Vasicek model (1977) is one of the earliest stochastic models of the term structure of interest rates. This model, though it has it's shortcomings, has many advantages, such as analytical tractability and mean reversion features, and may be viewed as a short rate model template.Several short rate models have their foundations rooted in the Vasicek model. The classical Hull-White model (1990a), for example, is an extension of the Vasicek model with time dependent parameters.In the work that follows we derive the short rate implied by the Vasicek model using the integrating factor method and provide an overview of this method and it's shorthand. Secondly we consider the model dynamics and finally we apply the model to zero-coupon bond pricing and provide a detailed derivation. Finally in reviewing the Vasicek model we outline it's disadvantages, consider other short rate models and look at the Hull-White extension to this model. The aim of the paper is to provide an overview of the Vasicek model and an introduction into short rate modelling.