THE CURRENT CREDIT CRUNCH is the first in which mathematical models have played an important role. Common flaws in risk models link the failure of rating agencies to predict the level of defaults on subprime mortgages, the freezing up of the market for complex debt securities and problems at several dozen hedge funds and a handful of banks, including the U.K.'s Northern Rock. We handed over the job of assessing financial risk to mathematicians and physicists -- and they failed.

The most popular of the quantitative risk management tools widely used by institutional investors and bankers is the value-at-risk (VaR) model. It seeks to estimate the maximum loss a portfolio of equities, loans or other securities is likely to experience over a given period. Since J.P. Morgan & Co. first developed it in the early 1990s, VaR has swept through the world of finance. It is endorsed in the Basel II banking regulations as a...