Academic journal article Journal of Financial Education

The Formula That Felled Wall Street? an Instructor's Guide to Default Modeling

Academic journal article Journal of Financial Education

The Formula That Felled Wall Street? an Instructor's Guide to Default Modeling

Article excerpt

Use of a one-factor model for the distribution of loan defaults has been repeatedly implicated in the Financial Crisis of 2007 - 2010, a.k.a. the Subprime Mortgage Crisis. Readers of articles in the business media are left with a host of questions. Just what exactly is this model, and what is the basis (if any) for the bold claim that it helped cause the Crisis ? This paper provides guidance for instructors seeking to help quantitative finance students understand the model, and to help them separate the wheat from the chaff in the media accounts implicating the model in the Crisis. I argue that commonly used procedures to estimate the model?s parameters were more to blame for the perceived model errors than the model itself, an insight missing in the media accounts.

(ProQuest: ... denotes formulae omitted.)


The Subprime Mortgage Crisis is the only significant economic event that our students are old enough to personally appreciate. The ongoing slack job market affects some of their parents and relatives, and looms over their own prospects upon graduation. While many factors played a role in the debacle, most analysts agree that the prospect of unexpectedly high defaults on mortgages, particularly among the riskier classes of mortgages, initiated a chain-reaction of subsequent events (e.g. the failure of Lehmann Brothers) that formed the Crisis.1

What role did quantitative modeling of defaults play (if any) in overvaluing subprime mortgage securities, thereby precipitating the Crisis? Popular accounts point a finger at the one-factor version of the Gaussian copula model, the outgrowth of an unusually influential research paper by David Li (Li, 2000). As noted by the Financial Times:

On August 10 2004, however, the rating agency Moody?s incorporated Li?s Gaussian copula default function formula into its rating methodology for collateralized debt obligations, the structured finance instruments that subsequently proved the nemesis of so many banks.. .A week after Moody?s, the world?s other large rating agency, Standard & Poor?s, changed its methodology, too.(Jones, 2009)

In an article titled ??Recipe for Disaster: The Formula That Killed Wall Street?, the on-line Wired Magazine (Salmon, 2009) asserted that ?Li?s copula function was used to price hundreds of billions of dollars? worth of CDOs fdled with mortgages.? This paper will develop the popular one-factor version of the Gaussian copula model and a simple spreadsheet implementation of it, for use by instructors who want to explore the aforementioned claims with students. Doing so will uncover (i) that the model default distribution is quite sensitive to changes in the model?s parameters and that (ii) while practitioners commonly estimate its parameters by finding parameter values implied by market prices of credit derivative securities, those estimates have proven to be unreliable. Hence we conclude that severe estimation risk, rather than model misspecification, is more likely the source of the model errors ridiculed in the business media.

The general importance of default distribution modeling and the notoriety it has achieved in the wake of the Crisis makes it particularly relevant for students today. The practical relevance implied by this notoriety may help motivate students to master difficult quantitative methods that might otherwise seem dry and technical. Becker and Greene (2001, p. 172) noted that studies of statistics and econometrics courses found that while problem sets were used more frequently than in less quantitative courses,

...those applications are rarely based on events reported in the financial newspapers, business magazines, or scholarly journals in economics... .Headline grabbing events in the news can often be used to engage students in applications that establish the importance of economics and statistics for use in real situations.

Root, Rozycki, Senteza, and Suh (2007) reported that at least one course in statistics is required for finance majors at 98% of the AACSB institutions, and that two statistics courses are required by 43% of those schools. …

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