Empirical Implementation of a 2-Factor Structural Model for Loss-Given-Default

by Michael Jacobs, Jr. of the Office of the Comptroller of the Currency

March 2011

Abstract: In this study we develop a theoretical model for ultimate loss-given default in the Merton (1974) structural credit risk model framework, deriving compound option formulae to model differential seniority of instruments, and incorporating an optimal foreclosure threshold. We consider an extension that allows for an independent recovery rate process, representing undiversifiable recovery risk, having a stochastic drift. The comparative statics of this model are analyzed and compared and in the empirical exercise, we calibrate the models to observed LGDs on bonds and loans having both trading prices at default and at resolution of default, utilizing an extensive sample of losses on defaulted firms (Moody's Ultimate Recovery Database™), 800 defaults in the period 1987-2008 that are largely representative of the U.S. large corporate loss experience, for which we have the complete capital structures and can track the recoveries on all instruments from the time of default to the time of resolution. We find that parameter estimates vary significantly across recovery segments, that the estimated volatilities of recovery rates and of their drifts are increasing in seniority (bank loans versus bonds). We also find that the component of total recovery volatility attributable to the LGD-side (as opposed to the PD-side) systematic factor is greater for higher ranked instruments and that more senior instruments have lower default risk, higher recovery rate return and volatility, as well as greater correlation between PD and LGD. Analyzing the implications of our model for the quantification of downturn LGD, we find the ratio of the later to ELGD (the "LGD markup") to be declining in expected LGD, but uniformly higher for lower ranked instruments or for higher PD-LGD correlation. Finally, we validate the model in an out-of-sample bootstrap exercise, comparing it to a high-dimensional regression model and to a non-parametric benchmark based upon the same data, where we find our model to compare favorably. We conclude that our model is worthy of consideration to risk managers, as well as supervisors concerned with advanced IRB under the Basel II capital accord.

JEL Classification: C15, C25, G33, G34.

Keywords: LGD, credit risk, default, structural model

Published in: Journal of Financial Transformation, Vol. 31, (March 2011), pp. 31-43.

Previously titled: A Two-Factor Structural Model of Ultimate Loss-Given-Default: Capital structure and calibration to corporate recovery data

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