# LIBOR rates from Vasicek/Hull-White model?

I am somehow puzzled by the following problem: LIBOR rates are forward rates for an interbank loan for 1M or 3M (let's limit the range of possibilities to these two cases). Assuming that I have estimated the parameters of any short-term model (Vasicek, Hull-White etc.) and simulate the paths of instaneous rates, can I model market-observed LIBOR 3M as integral of instaneous rates over 3M span and similarly LIBOR 1M as integral over 1 month of instaneous rates?
Or there is no link between market-observed LIBOR rates and instaneous rate that is modelled in the short-rate framework. Help me out!

Regards, Bart