May 12th, 2005, 4:13 pm
Usually in securitisation models you simulate the cash flows from your assets and deduct losses from this amount. The losses occur with some probability distribution, so you can do a monte carlo simulation to find out when the loss occurs and how bad it is.This will give you your expected cash flows from the deal.The merton model (I think) assumes that asset values follow a GBM and that once they fall below the fixed value of the debt the company has, there is a deafult (you will have to make an assumption about recovery rates)So, the probability of deafult is P(A<D)which is N(d1) from the BS model. This only gives you the probability that at maturity there is a default. (it doesn't tell you anything about before maturity)One improvement to be made on this is to model the probability using the distribution for stopped processes (from Barrier options)This will capture the probability that there has been a default before maturity. (See Bjork for the distribution)(You could, of course simulate the asset process, for each run, and when it falls below D (the debt level) you have a default at that point in time)...Sorry. this is a bit confused... maybe you should just use Google!Good luck