Dresdner publishes Gaussian copula model

Dresdner Kleinwort has released the latest in the series of structured credit models it is making publicly available along with a report describing the model. This week, the bank turns from factor models to the copula models that are the workhorse of CDO pricing. Models that do not rely on factors need more complex calculations using Monte Carlo techniques to simulate joint default events.

Copulas are the market’s choice to model the dependency structure inherent in credit portfolios because of even complex dependency structures can be incorporated into a generic model in a simple and intuitive way. Dresdner has published the model using Gaussian (normal) distribution and the Student T variation.

Although copula models using Monte Carlo simulation are often regarded as complex, Dresdner points out that they are nothing more than a simple algorithm or set of rules. The report describes the "Monte Carlo cookbook recipe" as follows:

1 Draw a random number for each credit
2 Generate dependent default times using the copula of choice
3 A given tranche experiences a default event, resulting in a principal loss, if the total loss corresponding to the number of defaults occurring before the tranche’s maturity is higher than the attachment point
4 For each tranche, store the present value of losses
5 Repeat n times, where n is the number of simulations

Once finished:

1 Calculate the expected loss for each tranche, by summing all discounted losses and dividing this by the number of simulations
2 Calculate the DV01
3 Divide the tranche expected loss by the DV01 to arrive at the fair spread.

The report goes on to describe some of the alternative copulas that have been used such as the Gumbel and Clayton copulas which are examples of Archimedean copulas.