Drift and Mean Reversion in Short-Rate Models
Summary
The document explains the drift term in a simple short-rate stochastic model and relates it to a broader family of interest-rate models. In the stated model, the drift is a constant contribution to the rate’s expected change over time, while the random term represents uncertainty. With no randomness, a positive constant drift would make the modeled rate rise continuously.
The answer places this model within a more general specification where the conditional mean and variance of rate changes can depend on the current rate. It notes that many models use a negative level-dependent coefficient to produce mean reversion. This is a conceptual explanation rather than an empirical comparison: it gives no calibration, data, or worked numerical example, and the simplified constant-drift model is not presented as a realistic long-run description of rates.
Key ideas
- In the simplified short-rate model, the drift term represents the rate’s expected change over time.
- A constant positive drift without randomness implies continued rate growth in the model.
- More general short-rate models can make expected changes depend on the current rate.
- A negative level-dependent coefficient produces mean-reverting behavior.
Tags
Full text
# What is drift in interest rate term structure model # What is drift in interest rate term structure model 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 by phdstudent (score 2) https://quant.stackexchange.com/a/23215 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.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.