Discrete Term Structure Models

Overview

Term structure models are statistical models that seek to explain why the term structure is what is and how it evolves in a statistical sense. Most often, this is done in order to quantify the risks in the term structure, usually for the purpose of hedging interest rate derivatives.

Short Rate Models

Short rate models are models of the short rate (usually the shortest available rate, such as the overnight, but at times as long as 3 months). The model describes the dynamics of the short rate, i.e. the statistical evolution of the rate.

The value of longer rates on the curve can be derived from the statistics of the short rate using risk neutral arguments. Therefore, short rate models are simple models that provide a description of the entire term structure. These models are useful because of their simplicity, but at the same time, they arent able to fully capture the term structure dynamics, so they represent something of an idealization.