Typically once the probabilities of each state are known, a simple uniform pseudo-random variable can be drawn.  Then, this can be used to determine what the simulated state will be.  This is repeated for each of the horizons.  Usually these are models so the probabilities of each state will usually change over time.   This is true for a Monte Carlo State Transition model, but not a Markov Chain State Transition model.  In the Markov Chain, the instrument, or loan, will proportionally go to all states.  in the Monte Carlo it will only go to one.   For example, if the PRN was 0.8, then it would remain current.  If the PRN was 0.995, it would go to Prepay.  Hope that helps. ... View more