Tuesday, March 10, 2009

Mathematical Model and the Mortgage Mess

From the New York Times:

There was no mathematical elegance to the mortgage-backed securities that helped lead to the market crash of recent months. In these deals, interest and principal payments from mortgages were bundled into different packages called tranches, each with different risks and interest rates.

The only tricky part of these deals, quants say, was in estimating how often people would default on these mortgages, and how correlated those defaults were. For that you need a model. The more people act in concert, the less diversity in your investment and the greater the chances of disaster. The model for correlation came from other securities in which corporate bonds were pooled in tranches. In 2000, David X. Li, a banker with a doctorate in statistics who was then at RiskMetrics, part of J. P. Morgan Chase, began using mathematical functions called Gaussian copulas to estimate the likelihood of corporations’ dying in unison. (It was an idea borrowed from the life insurance industry, where copulas measure the correlations between deaths of spouses.)>>>MORE