# Why is the mean time-dependent in the Hull-White interest rate model?

In the Vasicek interest-rate model, the interest rate reverts to a constant mean. This makes sense to me. In my conception, the mean ought to be time-invariant, since interest rates don't follow an increasing or decreasing trend in the long term.

In the Hull-White modified model, the mean is a time-dependent function. I cannot understand why this is the case.

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Since when are interest rates insulated from time-varying changes? tradingeconomics.com/united-states/interest-rate (chose the start date to be 1971, long-term enough?) –  Matt Wolf Aug 2 '13 at 2:46
@MattWolf Thanks for the link. I didn't mean to suggest that rates don't vary with time, but that the rate mean doesn't vary with time. For example, in this chart, rates have an average around 5% –  tjahrenholz Aug 2 '13 at 21:11
the choice of model always should be determined by the specific use case. If you model product with a duration of 30-50 years then sure you are most likely right to assume a long-term mean of around 5%. But if you look to model interest rate products with, let's say, 2 years of maturity then you should hardly plug in a 5% rate in this current environment. Hence some models assume a time varying mean. –  Matt Wolf Aug 3 '13 at 2:24