Signs of the apocalypse

February 24, 2009 in Finance,Math,Risk

Wired has published an article attacking the Gaussian copula: Recipe for Disaster: The Formula That Killed Wall Street.

It's a very typical "hate the game, not the player" article which finds fault with a tool rather than the people who use it. Not that I completely disagree with the critique - but imagine my surprise when an idea rooted in that obscure statistical field in which I claim expertise showed up on the [digital] glossy front page of a pop sci magazine.

It seems like the Gaussian copula is the new VaR - everyone uses it, everyone claims to know its limitations, but when the world blows up everyone is quick to point fingers at the model. From a mathematical perspective, the two are actually incredibly close, which is perhaps unsurprising given their pitch of "easy risk measurement with minimal parameterization." VaR has dubious use as a relative indicator through time - if day 2's VaR is higher than day 1's VaR, maybe risk increased. But as soon as one applies meaning to the VaR, they have overstepped its utility. The Gaussian copula has similarly limited value - under its assumptions, one can gauge the relative magnitude of risk and price shocks.

In truth, we use oversimplifications like this all the time in finance, in places few pop sci magazines dare tread. Case in point: options pricing. Volatility, like correlation in the Gaussian model, is a plug - it's the number that gets you to the right place. It has no meaning outside a log-normal no-arbitrage zero-drift tax-free world. And yet we use it just fine.

The Gaussian copula may be a poor fit to reality, but it's good math. It's simple and gets a reasonable approximation. In the next month the credit world will officially adopt a newly open-source JP Morgan model for all CDS pricing. Like the Gaussian copula and VaR - two other JP Morgan innovations - this model oversimplifies the world in order to provide an easy view of pricing and risk. Does that make it bad? Certainly not. The fault is with the trader, risk manager, or analyst who blindly adopted the model without thought.

Surely if a man with an exotic flamethrower accidentally burnt his village down, we would blame the man and not the unfamiliar machine for causing the damage.

I'm definitely not a supporter of the financial applicability of the Gaussian copula - I spent a good chunk of my academic career ranting against it - but, just as with VaR, much of the the fault lies with the users and not the mathematics.

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