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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 ...

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