Risk Analysis of Collateralized Debt Obligations
by Kay Giesecke of Stanford University, and
March 3, 2010
Abstract: Collateralized debt obligations, which are securities with payoffs that are tied to the cash flows in a portfolio of defaultable assets such as corporate bonds, play a significant role in the financial crisis that has spread throughout the world. Insufficient capital provisioning due to awed and overly optimistic risk assessments is at the center of the problem. This paper develops stochastic methods to measure the risk of positions in collateralized debt obligations and related instruments tied to an underlying portfolio of defaultable assets. It proposes an adaptive point process model of portfolio default timing, a maximum likelihood method for estimating point process models that is based on an acceptance/rejection re-sampling scheme, and statistical tests for model validation. To illustrate these tools, they are used to estimate the distribution of the profit or loss generated by positions in multiple tranches of a collateralized debt obligation that references the CDX High Yield portfolio, and the risk capital required to support these positions.
Keywords: Correlated default risk, collateralized debt obligation, portfolio credit derivative, actual measure, point process, intensity, re-sampling, thinning, acceptance/rejection sampling, exact simulation.
Published in: Operations Research, Vol. 59, No. 1, (January-February 2011), pp. 32-49.