Hobbies And Interests
Sklar's Copula
A. Sklar was the first to introduce the use of copulas in 1959, and recent applications of copulas in biology, biostatistics, hydrology, and finance have emerged. Copulas are a standard tool in the modern financial industry for risk management, modeling credit portfolios, and multi-asset pricing for complex derivatives.
Copulas Used in the Insurance Industry
The insurance industry uses a family of copulas to assess risk. Following the September 11, 2001 terrorist attacks, the application of copulas emerged as a tool for solving the problem of risk accumulation. As of 2011, three types of copulas are used in the insurance industry: the normal copula, the student copula, and the Gumbel copula.
The Gaussian Copula
The application of the Gaussian copula for credit derivatives is considered one of the root causes of the financial crisis of 2008 and 2009. A Gaussian copula refers to a normal distribution of variables (a bell curve) and can be used to predict the behavior of more than one variable under the curve. However, there are specific limitations of the Gaussian copulas. They lack dependency dynamics and give a poor representation of extreme events. In 2006, Merrill Lynch held a conference in London specifically to address these limitations and several statisticians proposed models to rectify them. A paper on the conference -- the ̶0;Credit Correlation: Life After Copulas̶1; -- was published by World Scientific in 2007.
The Gaussian Copula & the Financial Crisis
In 2009, Susan Lee published "A Formula From Hell." In her article, Lee suggests blame for the financial meltdown extends across the financial industry form Alan Greenspan, to Richard Fuld, and to a variation of the Gaussian copula function developed by David X. Li. Li earned a PhD in statistics in Canada before he was hired by JP Morgan Chase. Li arrived at an application of the Gaussian copula that figures the probability that all individual debt securities will fail at once. Li named this value the default correlation. The correlation was heavily relied upon to cut corners and enabled the use of proxies for credit default swaps rather than actual data. Before anyone was aware there was a problem, the value was used to quantify risk for complex financial instruments, embraced by the regulatory frameworks of the financial industry, and used to determine capital requirements for credit structures at major banking institutions. In combination with subprime mortgages and risky credit decisions by individuals and banks, the mix was a recipe for disaster.