Financial Engineering, CDOs & Gaussian Copula

I was talking to an old friend last night. Our conversations led to us talking about Collateralized Debt Obligations (CDOs) and Collateralized Mortgage Obligations (CMOs) and the financial crisis. I referred him to this article from Wired Magazine on CDOs, titled Recipe for Disaster: The Formula that killed Wall Street. It does a pretty good job of explaining the CDO problem.

http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all

We were talking about what went wrong and how we got into this state. A lot of the blame has fallen on the quants that created many of these products. Since I have a Masters in Financial Engineering, my buddy asked me if it was true.

My belief is that I think the quants tried their best to come up with pricing and formulas for a lot of the products out there. There are a lot of limitations as to what they understood and could predict. I'm not too sure if they communicated these limitations through to management and the sales team properly. Or if the management just over simplified these limitations or they just ignored it since they couldn't understand it. But somewhere along the line, these limitations were lost. And people took the math as the gospel truth. No where is this more evident than in CDOs.

Just a short summary of the above article for those of you who are interested.

For those of you that are unfamiliar with CDOs (Collateralized Debt Obligations). Basically, CDOs are pools of different types of debt all lumped into one. You have car loans, credit card debt, slices of housing loans (probably bottom tranches of CMOs), etc. You get the idea.

Now Wall Street had a problem - how to price these things? The issue was there was a lack of data on defaults and default correlations of these varied pools of debt. No one knew the historical default data and the correlation rates. So how do we go about pricing them?

Enter David Li. A bright quant working for JP Morgan Chase. He wrote an article called "On Default Correlation - A Copula Function Approach". Li came up with a way to figure out the correlations without historical data. He used these instruments called Credit Default Swaps (CDS). A CDS is a way of insuring your debt. ie if you own a bond or type of debt and you were afraid that the borrower couldn't pay back the debt, you bought a CDS, a kind of default protection. Li reasoned that the CDS of various debt pools/ instruments are a good approximation for historical default rates after all CDS are meant as protection for defaults of those debt pools/ instruments. Li now has a method of pricing CDOs. The formula used to price CDOs is the Gaussian Copula.

The effect was to energize the CDO market. Now people could put a price to these pools of debt, they could sell them or trade with them. They used the formula everywhere. They priced hundreds of billions of dollars of CDOs with it. A lot of the banks realized that the debt was very sensitive to the rise or fall of housing prices. No one put a stop to raised a flag because selling CDOs were so profitable. Furthermore, the managers who were empowered to stop this did not fully understand the math behind the problems and did not fully understand the various arguments.

So we are here today. The housing market blew up. The CDO/ CMO market blew up. Billions lost.

Will we learn from our mistakes? I don't think so. We'll probably make some new variation of the old mistake.