Frenzied Copula-tion

A lot of people know that financial firms used a lot of incorrect mathematical models during the run-up to the recent financial crisis. But a lot of people don't know what exactly those models were. Other uninformed people - myself included - assumed that the models were some form of the famous Black-Scholes option pricing algorithm, invented (strangely enough) by a guy named Robert Merton, which gives the price of an option based on the price of a stock.

Now, it's true that Merton, along with Myron Scholes, was a director of the disastrously failed hedge fund Long Term Capital Management. And it is true that Robert Merton, at least in his online photos, uses an almost unimaginable amount of hair grease. But it turns out that the real formula that was being used was something entirely different, called the "Gaussian copula". This is a formula for calculating correlations between housing prices in different areas (i.e. the components of a CDO). It asumes the correlation is constant - something that is usually only close to true when markets are going in one direction, and not at all true when markets change direction. So this was the formula that famously assumed that "housing prices will never go down."

Here is a very interesting article about how this relatively useless formula became so universal on Wall Street, although the article doesn't go into the math. But if you ever want to sound smart at a party, now you know the Achilles' Heel of the former titans of finance - the Gaussian cupola.