What is drift in interest rate term structure model

Question

I was studying about the interest rate term structures and i came across term structure model with (and without) drift.

I am really unsure about what this drift is in this equation for term structure model. $$dr=\lambda dt + \sigma dw$$

From the equation above $\lambda$ is the drift factor and $\lambda dt$ is the drift. I have a very confusing explanation of drift which is along the lines of interest rates are moved in the future by some factor.

Can someone give me an explanation of drift. An example associated with it would be ideal. Thanks!

Answer 1

Many term structure models-both single-factor and multifactor imply dynamics for the short-term riskless rate $r$ that can be nested within the following stochastic differential equation:

$dr = (\alpha + \beta r)dt + \sigma r^\gamma dZ. $

These dynamics imply that the conditional mean and variance of changes in the short-term rate depend on the level of $r$.

On your case we have $\alpha = \lambda$ and $\beta=\gamma=0$, and the model simplifies to the one on Merton (1973). So $\lambda$ is just capturing the growth over time of the interest rate. If there was no uncertainty, it would mean that interest rates would grow forever. Usually we don't see this in the data that's why most models haave a $\beta < 0$ which implies that interest rates are mean reverting.