When simulating stocks one can easily use GBM with only one random variable per simulation to create a new stock price in say 5 years, you don't need to create the whole asset paths if you don't need that.
Now I wonder if that is also the case for the Vasicek model. Can I use the Vasicek short rate model with only one random variable per simulation to create a new short rate in 5 years (without constructing the whole path to the short rate in 5 years?).
If so, how do you go from the new simulated short rate to the whole new yield curve?