# The One-Factor Gaussian Copula Model – Too Simplistic?

## Gunter Meissner

“Make everything as simple as possible, but not simpler”

– Albert Einstein

In Chapter 6 we discussed the standard copula model. It joins n marginal distribution to a single n-variate distribution. The n marginal distributions are correlated in a correlation matrix. This matrix is n × n dimensional, so if the CDO has 125 assets, the matrix is 125 × 125 dimensional. This is mathematically and computationally quite challenging. Often financial institutions take a shortcut, putting the assets into sectors and correlating the different sectors. This reduces the dimension of the correlation matrix.

A further shortcut is to assume that all assets in the portfolio have the same pairwise correlation. This seems simplistic, and it is. However, if the assets in the portfolio are homogeneous – ie, they are very similar, for example they have the same or similar credit rating and/or they belong to the same sector – this assumption may be tolerable.

If we simplify further, we can also assume that the default probability of all assets in the portfolio is the same. This again seems simplistic and it again is. However, if the assets in the portfolio are homogeneous – ie, they have