Martingale Models for the Short Rate

Abstract

This chapter is devoted to an overview and analysis of the most common short rate models, such as the Vasiček, Dothan, Hull–White, and CIR models. These models are analyzed and classified from the point of view of positive short rates, normal distribution, mean reversion, and computability. In particular we present the theory of affine term structures, and discuss the inversion of the yield curve. Analytical results for bond prices and bond options are presented for all the affine models.