Overview
Short rate models are models of a short term interest 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, that is the statistical evolution of the rate over time. The values and dynamics of longer rates on the curve can be derived from the those of the modeled rate using risk neutral arguments.
These models are useful because of their simplicity, but at the same time arent able to fully capture the term structure dynamics in a realistic fashion, so they represent something of an idealization.
Generic Model
The generic model is a generic functional form of various short rate models listed below.
{% dr = u(r, t) dt + v(r, t) dW %}
(wilmott sect. 16.2)
Mathematical Tools
- Implementation - methods of implementation.
- Recovering the Term Structure shows how the short rate model can be used to construct the rest of the term structure.
- Risk Neutral Valuation - demonstrates how the short rate model can be used to price interest rate derivatives using risk neutral arguments.