The transaction consists of $100mm of imaginary one period mortgage assets. During the course of the one period (think one year), the assets can either make their full payment or default. There is a fixed probability for each loan to default, but the defaults of the loans are correlated. (Equivalently there is a common driving factor contributing to defaults for all loans.) Figure 1 shows the distribution of defaults from this simple model. All three lines show the distribution of defaults of 10%. That is, the average of the results is the same for all three curves. The lines differ in the amount of correlation among the defaults on individual loans. Equivalently, each line reflects a differing amount of the common factor. The model also assumes that there is a very large number of loans in the pool. Note in this model there are no prepayments.

For the situation with low correlation, the probability of default is centered on the average value of 10% and looks much like a normal distribution. As the correlation increases, the distribution becomes more skewed. There is a substantial chance of low losses, but the chance of very high losses increases as well.

Figure 1.

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