Statistics for Finance

Chapter 10

Stochastic interest rate models

In this chapter, we shall provide a catalogue of a number of well-known models of interest rates as it is important to be familiar with these often referenced models and, in particular, their properties. The main focus is on univariate stochastic differential equations or one-factor models as they are called in the financial literature because only one state variable (or factor), r(t), is used to describe variations in the interest rate.

Conceptually r(t) is the continuously compounded interest rate of risk-free financial securities, which was introduced in Section 2.3. Thus r(t) denotes the instantaneous interest rate or the spot rate obtained by investing in a riskless security in the time interval ...