A Comparative Analysis of the One-Factor Gaussian Copula and the One-Factor Student t Copula Applied to Synthetic CDO Valuation: A Financial Crisis Perspective

Abstract

In the aftermath of the financial crisis of 2007-2009, the Gaussian copula has received a lot of negative attention concerning its role in the valuation process of Collateralized Debt Obligations (CDOs). Specifically, by generating the portfolio loss distribution, the application of this model allowed its users to quantify the risk in the portfolio of assets underlying the CDO. However, because of its underlying distributional assumption, the Gaussian copula critically underestimates the probability of many simultaneous defaults, and thus the risk associated with the most senior CDO tranches. This Master’s Thesis considers the use of the one-factor Gaussian copula applied to synthetic CDO valuation, and compares it to an alternative represented by the one-factor Student t copula. Through a semi-analytical implementation of the one-factor Gaussian copula, and a Monte Carlo implementation of the one-factor Student t copula, this thesis finds that the Student t copula, due to its fatter-tailed nature, distributes the relative risk between tranches somewhat differently. In general terms, the one-factor Student t copula assigns more risk to the most senior tranche in the CDO and less risk to the equity tranche. In spite of this difference, no immediate improvement is obtained in relation to matching the observed tranched ITraxx Europe quotes, and thus in the ability to simultaneously price all synthetic CDO tranches correctly. Through a thorough sensitivity analysis of both models, the researcher finds it unlikely that the specifics of the Gaussian copula played a significant role in the escalation of the financial crisis. The similarities between the behavior of the two models under varying input assumptions indicate that no major improvement would have been obtained, had the one-factor Student t copula been applied as the market-accepted valuation model. Instead, it appears that other underlying factors within the financial industry were the main contributors to the outbreak of the crisis, and that math represented by the Gaussian copula, was used as an excuse to justify some of the unhealthy and immoral behavior that occurred across the financial industry. This, both in relation to some very concerning moral hazard problems within financial institutions, the inevitable conflict of interest that exists in the business model of the credit rating agencies, and the general overconfidence, which dominated across the financial industry during this period.