Tuesday, February 24, 2009

Tales from the Meltdown 11: The Quants

The Gaussian copula allows the user to assess the joint risk of a pair of events happening (e.g., the default of two mortgages), given an understanding of their correlation. The method was widely used in the financial world for the pricing of structured products and default swaps. Unfortunately for all of us, at least three things are wrong with the model: there is typically insufficient historical data to assess the default risks of the underlying (we just don't know enough about their behavior under different states of nature), the assumed distribution of these risks is actually non-normal (probably closer to a power law distribution with fat tails, per Mandelbrot), and the correlation between securities is non-linear (particularly true of downside events: as the meteor strike gets big enough, everyone is in for an extremely bad day).

Felix Salmon discusses the widespread use, and ultimate failure of the Gaussian copula method in the new issue of Wired:

"The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.

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