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.


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:

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

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    $\begingroup$ Thank you! This clears up a lot. $\endgroup$ – Michael Jul 23 '19 at 15:09
  • $\begingroup$ Welcome :) Could you accept the answer if it answers your question? Thanks. $\endgroup$ – byouness Jul 24 '19 at 7:03

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