Li's paper "On Default Correlation: A Copula Function Approach"[3] was the first appearance of the Gaussian copula applied to CDOs published in 2000, which quickly became a tool for financial institutions to correlate associations between multiple financial securities.[2] This allowed for CDOs to be supposedly accurately priced for a wide range of investments that were previously too complex to price, such as mortgages.
However, in the aftermath of the global financial crisis of 2008–2009 the model has been seen as a "recipe for disaster".[2] According to Nassim Nicholas Taleb, "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked. Co-association between securities is not measurable using correlation"; in other words, "anything that relies on correlation is charlatanism."[2]
Li himself apparently understood the fallacy of his model, in 2005 saying "Very few people understand the essence of the model."[9] Li also wrote that "The current copula framework gains its popularity owing to its simplicity....However, there is little theoretical justification of the current framework from financial economics....We essentially have a credit portfolio model without solid credit portfolio theory."[10] Kai Gilkes of CreditSights says "Li can't be blamed"; although he invented the model, it was the bankers who misinterpreted and misused it.[2]
Li's paper
Li's paper is called "On Default Correlation: A Copula Function Approach" (2000), published in Journal of Fixed Income, Vol. 9, Issue 4, pages 43–54.[9][3] In section 1 through 5.3, Li describes actuarial math that sets the stage for his theory. The mathematics are from established statistical theory, actuarial models, and probability theory. In section 5.4, he uses Gaussian copula to measure event relationships, or mathematically, correlations, between random economic events, expressed as:
In layman's terms, he proposes to quantify the relationship between two events "House A" defaulting and "House B" defaulting by looking at the dependence between their time-unit-default (or survival time; see survival analysis). While under some scenarios (such as real estate) this correlation appeared to work most of the time, the underlying problem is that the single numerical data of correlation is a poor way to summarize history, and hence is not enough to predict the future. From section 6.0 onward, the paper presents experimental results using the Gaussian copula.