SAS MIP Monte Carlo Simulation - Transition Matrix

[Mantripragada]

Hello,

Can someone explain to me the process of Monte Carlo simulation?

Example:

Marcov Chain transition matrix (Mortage model)

CtoD model: Current to Delinquent (Logistic Model)

CtoP model: Current to Prepay (Logistic Model).

Converting to multinomial format

P[Current] = 1/(1+CtoD + CtoP)  = 0.96

P[Delinquent] = CtoD/(1+CtoD + CtoP)  = 0.03

P[Prepay] = CtoP/(1+CtoD + CtoP) = 0.01

At first projection month, how are these probabilities converted to 1,0,0 (0r 0,1,0 or 0,0,1)?

Using uniform distribution and decide if the probability is less than 0.96 then the loan will be current (C =1, 0, P=0)?

Just wanted to understand the conversion of probabilities to a unique state.

Thanks

R.

[Stochastic_142 · Accepted solution]

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.

[Mantripragada]

Thanks for the clarification. Clearly stating in terms of my problem - may help someone.

Random number LE 0.96 then current

Random Number GT 0.96 but LE 0.99 then delinquent

Random Number GT 0.99 but LE 1 then Prepay

Thank you very much!