What is meant by a normal model of interest rates?

Question

What will be an ideal response?

Answer 1

The classification of a model as normal is based on the assumed dynamics of the random component of the stochastic differential equation (SDE). Normal models assume that interest rate volatility is independent of the level of rates and therefore admits the possibility of negative interest rates. More details are given below.

Consider a basic continuous-time stochastic process for describing the dynamics of the short rate given by:
dr = bdt + ?dz

where dr and dt are the change in the short rate and time, z is a random term with dz denoting
a random process, ? is the standard deviation of the changes in the short rate, and b is the expected direction of rate change. In the Vasicek specification, volatility is independent of the level of the short rate as in the above equation and is referred to as the normal model. Independence implies that it is possible for negative interest rates to be generated. The Ho-Lee model is also a normal model because volatility is independent of the level of the short rate. The Hull-White model is also a normal model where volatility does not depend on the short rate but, unlike the Ho-Lee model, it allows for mean reversion.

Empirical evidence suggests that the normal model is a suitable model because the assumption about the independence of volatility relative to the short rate is generally a valid assumption. An exception is when the short-rate is greater than ten percent.