Negative Libor Simulation

Question

Can LIBOR rates be simulated using short rate models? If no, what is the reason behind it?

What is a simple model to simulate LIBOR rates? Especially in a negative rate environment.

Answer 1

Yes, LIBOR rates can be simulated using short rate models. Or rather, Libor rates can be obtained from simulated short rate values.

Usually, you have formulas giving you the zero-coupon bond price as a function of the short rate. For affine models for example, this would be of the form: $$P(t, T) = e^{A(t, T) - r(t)B(t,T)}$$ (for example, for the one-factor Hull-White model, see: https://quant.stackexchange.com/a/31998/26242)

Then, the Libor is deduced from the zero bond could be done using its definition:

$$P(t, t + \delta) = \frac{1}{1 + \delta L(t, \delta)} \iff L(t, \delta) = \frac{1}{\delta}\left(\frac{1}{P(t, t+\delta)} - 1\right)$$