The Copious Copula Blame Game

Seems the infamous mathematical probability distribution function, the Gaussian Copula, is at the forefront of controversy once again. It seems those financial engineers, the Quants, the ones who use advanced probability and statistics to model financial markets, upon whose work many derivatives are based, knew the use of Gaussian Copulas was fundamentally flawed.

Pricing a CDO - Not only Bad Math, Bad Computation too

A working paper, Computational complexity and informational asymmetry in financial products, Sanjeev Arora, Boaz Barak, Markus Brunnermeier, Rong Ge. sheds some light on the complex mathematical models upon which credit default obligations and other derivatives are based.

What Arora et al. prove is not only are many derivative mathematical models impossible to compute, never mind in real time, because they require more computing power than the world possesses, the missing information to run a mathematical model is a very good place to cheat with.

To understand what CDOs, derivatives are, see this post, complete with video tutorials. For some background on the mathematics behind derivatives, read We Want the Formula and this one on some of the probability functions.

Onto the paper. Firstly this quote:

One of our main results suggests that it may be computationally intractable to price derivatives even when buyers know almost all of the relevant information, and furthermore this is true even in very simple models of asset yields.

We want the formula, we want the formula, the actual equation of CDOs

Like the scene from the The Return of the Secaucus 7, earlier I was asking for details on the actual mathematics upon which derivatives, CDOs (Collateralized debt obligations) are based.

Wired Magazine has answered the call in the article Recipe for Disaster. This article outlines the actual mathematical formula, a Gaussian copula, upon which so many derivatives are based.

In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple math—by Wall Street standards, anyway—Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

You must read the entire article, yes they mention mathematics, but they are explaining it all in layman's terms.

One thing I did not know, pointed out in the article, is that there are no limits on the number of CDS (credit default swaps) that can be issued against one borrower. CDSes are literally unconstrained by are subject to mark-to-market.