An Option Theoretic Model for Ultimate Loss-Given-Default with Systematic Recovery Risk and Stochastic Returns on Defaulted Debt

Posted: 12 Feb 2010

Date Written: February 11, 2010


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, with stochastic drift. The comparative statics of this model are analyzed and compared to the baseline models having no independent recovery rate process. 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 in the period 1987-2008 (Moody’s Ultimate Recovery Database™), 800 defaults in the period 1987-2008 that are largely representative of the US 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 models and recovery segments, in particular that the estimated volatilities of recovery rates and of their drifts are increasing in seniority, in particular for bank loans as compared to bonds. Analyzing the implications of our model for the quantification of downturn LGD, we find the later to be declining in expected LGD. Finally, we validate the leading model derived herein 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.

Keywords: Recoveries, Default, Loss Given Default, Financial Distress, Bankruptcy, Credit Risk, Basel, Distressed Debt

JEL Classification: G33, G34, C25, C15, C52

Suggested Citation

Jacobs, Michael, An Option Theoretic Model for Ultimate Loss-Given-Default with Systematic Recovery Risk and Stochastic Returns on Defaulted Debt (February 11, 2010). Available at SSRN:

Michael Jacobs (Contact Author)

PNC Financial Services Group ( email )

1 PNC Plaza, 249 5th Avenue
Pittsburgh, PA 15222-2707
United States

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