Am I doing this right?
Posted: June 27th, 2005, 9:54 pm
I need to simulate losses on a portfolio of N loans. Each of the loans amortises to zero over 10 years.I have one probability of default per year, a loss given default and an exposure at default for each loan. I also have an N x N asset correlation matrix.I'd like to check the method that I'm going to use to simulate losses occurring in any one year. I’d also like to check that I’m doing the right thing when I try and look at what happens over the 10 years, year by year.1) Firstly, I’ll generate a matrix of correlated asset values by (1) decomposing the asset correlation matrix, (2) creating a vector of asset values by random sampling from a normal distribution and (3) multiplying the decomposed matrix with the vector of random asset values to produce correlated asset values.Is it ok to use a normal distribution here to initially simulate asset values? I have opted to use it as it is by far the simplest. Do people usually write a section into their code to discard all values below zero as asset values cannot be negative?2) Next, I’ll take each probability of default and take the inverse of the cumulative distribution to get the point of default. I can then compare this with the correlated asset value to work out whether the asset has defaulted or not. If an asset has defaulted then I can easily calculate the loss by using loss = exposure at default * loss given default.I intend to run steps 1 and 2 thousands of times to build up a picture of what happens in one year. What about if I want to look at what happens over the 10 years, year by year. I guess I have to set it up so that an asset that defaulted in say the year 1 simulation does not appear in the year 2 simulation, or the year 3,or the year 4 etc. Does what I’m trying to do make any sense? Have I made any big mistakes in my stages? I really appreciate the help.
