risk modeling

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.

JPMorgan Say What?

wallstreetWhat a surprise, that biggest fighter against financial regulation of them all, JPMorgan Chase accrued a $2 billion dollar loss:

The $2 billion loss came from a complicated trading strategy that involved derivatives, financial instruments that derive their value from the prices of securities and other assets. JPMorgan said the derivatives trades were part of a hedge, meaning they were set up to offset potential losses on the bank’s large holdings of bonds and loans.

black swanThat loss was caused by derivatives and credit default swaps and in part due to a Value at Risk model. This is the same type of model which was part of the financial crisis and has been warned about repeatedly for not being mathematically complex enough to base one's gambling debts on. No surprise a VaR model was behind the loss.

It produced large losses even without extreme movements in the derivatives markets or underlying bond markets.

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.