Reducing Economic Risk: Mathematical analysis will play crucial role in restoring credit confidence
Credit market turmoil—driven by the sub-prime mortgage crisis and fueled by fallout from financial securities known as collateralized debt obligations—has led to huge banking losses in recent months and continues to rattle Wall Street.
“Early successes and handsome profits are at the root of a dangerous proliferation of dubious loans that were underwritten by banks and then sanctioned by overly optimistic rating agencies,” said Carmona, whose research explores the general mathematical framework of credit risk and examines methods for assessing extreme risk. He has developed a course on rare events and extreme risks.
“Given the complexity of these instruments, it is very difficult to assess their potential downsides—to tease out and anticipate the factors that contribute to a default.”
As such, departments like operations research and financial engineering at Princeton play a crucial role in restoring confidence in the markets. “We are able to investigate financial sector innovations in a way that, because of time and profit pressures, industry players cannot,” said Sircar.
Collateralized debt options, or CDOs for short, are packages of securities that are sliced into pieces, or “tranches,” and then sold to investors. The riskiest slices—those with the highest chance of default—earn the highest returns, while the safer tranches earn lower returns. One of the problems of the current credit crisis is that some tranches that looked to be quite safe are now considered dangerous.
Carmona and Sircar—whose research is funded by a National Science Foundation grant in conjunction with researchers at the University of Texas-Austin and the University of California-Santa Barbara—are creating mathematical models that capture the volatile nature of CDO markets while remaining computationally feasible. Although they plan to extend their study to other types of CDOs, thus far they have concentrated on financial instruments that are based on credit portfolio indexes and those backed by corporate bonds rather than home mortgages. The NSF grant also is funding an international conference for leading experts in credit derivatives that will be held in Princeton in May.
One of Sircar’s recent papers, written with former graduate student Evan Papageorgiou *07, outlines a credit derivatives model that measures the intensity of default risk in CDOs backed by corporate bonds. Trying to measure the risk of default in a pool of hundreds of firms, he says, is a problem that extends well beyond quantifying the risk of default for each individual company.
“Defaults are not independent events and they tend to cluster because of the contagious nature of economic stresses,” said Sircar. “If one firm fails, what does this mean for the others?” Sircar, whose graduate-level class in credit risk has doubled in size over previous enrollment, said students are very interested in understanding the current turbulence in financial markets. “Some days it feels as if I am teaching politics,” he said.
The role of the Department of Operations Research and Financial Engineering, according to Carmona and Sircar, is to help tame the Wild West landscape of financial-sector innovation so that risks are properly quantified to investors. About half of Ph.D. students from their department become academics and train future practitioners. Some graduates become traders; others become regulatory sheriffs. However, the majority of Ph.D.s going to industry become “quants,” practitioners of quantitative finance who analyze—in a highly technical way, because of their Princeton training—sophisticated instruments like CDOs.
Carmona and Sircar’s cutting-edge research in financial mathematics has informed their teaching, even at the undergraduate level. For example, Adam Epstein ’07 wrote a prize-winning senior thesis—finished several months before the credit-market crunch first hit in August—that addresses the urgent problem of modeling the credit derivatives market.
“It is important that our students learn not just about financial innovation but also how to look deeply into the downside of risk,” said Carmona.