Federal Dposit InsuranceCorporation• Center for Financial Researchh
Sanjiv R. Das
Darrell Duffie
Nikunj Kapadia
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
FDIC Center for Financial Research
Working Paper
No. 2009-05
Implied Recovery
November 2008
Empirical Comparisons and Implied Recovery Rates
kkk
An Empirical
An Empirical Analysis
State-
Efraim Benmel Efraim Benmelech May, 2005
June 20
May , 2005 Asset S2005-14
September 2005
Sanjiv R. Das
Darrell Duffie
Nikunj Kapadia
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
FDIC Center for Financial Research
Working Paper
No. 2009-05
Implied Recovery
November 2008
Empirical Comparisons and Implied Recovery Rates
kkk
An Empirical
An Empirical Analysis
State-
Efraim Benmel Efraim Benmelech May, 2005
June 20
May , 2005 Asset S2005-14
September 2005
Implied Recovery∗
Sanjiv R. Das
Santa Clara University
Santa Clara, CA 95053
Paul Hanouna
Villanova University
Villanova, PA 19085
November 7, 2008
Abstract
In the absence of forward-looking models for recovery rates, market participants
tend to use exogenously assumed constant recovery rates in pricing models. We de-
velop a flexible jump-to-default model that uses observables: the stock price and stock
volatility in conjunction with credit spreads to identify implied, endogenous, dynamic
functions of the recovery rate and default probability. The model in this paper is par-
simonious and requires the calibration of only three parameters, enabling the identifi-
cation of the risk-neutral term structures of forward default probabilities and recovery
rates. Empirical application of the model shows that it is consistent with stylized fea-
tures of recovery rates in the literature. The model is flexible, i.e., it may be used with
different state variables, alternate recovery functional forms, and calibrated to multi-
ple debt tranches of the same issuer. The model is robust, i.e., evidences parameter
stability over time, is stable to changes in inputs, and provides similar recovery term
structures for different functional specifications. Given that the model is easy to un-
derstand and calibrate, it may be used to further the development of credit derivatives
indexed to recovery rates, such as recovery swaps and digital default swaps, as well as
provide recovery rate inputs for the implementation of Basel II.
JEL Codes: G0, G1.
∗Thanks to the editor Carl Chiarella, an Associate Editor, and two anonymous referees for very useful
guidance on the paper. We are grateful to Viral Acharya, Santhosh Bandreddi, Christophe Barat, Darrell
Duffie, Lisa Goldberg, Francis Longstaff and Raghu Sundaram, as well as seminar participants at Barclays
Global Investors, Moodys KMV, Standard & Poors, University of Chicago’s Center for Financial Math-
ematics, and the American Mathematical Society Meetings 2008, who gave us many detailed and useful
suggestions. We are grateful to RiskMetrics for the data. The first author received the financial support of
a Santa Clara University grant and a Breetwor fellowship. The authors may be contacted at: Sanjiv Das,
Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, Email: srdas@scu.edu. Paul Hanouna,
Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, Email: paul.hanouna@villanova.edu.
1
Sanjiv R. Das
Santa Clara University
Santa Clara, CA 95053
Paul Hanouna
Villanova University
Villanova, PA 19085
November 7, 2008
Abstract
In the absence of forward-looking models for recovery rates, market participants
tend to use exogenously assumed constant recovery rates in pricing models. We de-
velop a flexible jump-to-default model that uses observables: the stock price and stock
volatility in conjunction with credit spreads to identify implied, endogenous, dynamic
functions of the recovery rate and default probability. The model in this paper is par-
simonious and requires the calibration of only three parameters, enabling the identifi-
cation of the risk-neutral term structures of forward default probabilities and recovery
rates. Empirical application of the model shows that it is consistent with stylized fea-
tures of recovery rates in the literature. The model is flexible, i.e., it may be used with
different state variables, alternate recovery functional forms, and calibrated to multi-
ple debt tranches of the same issuer. The model is robust, i.e., evidences parameter
stability over time, is stable to changes in inputs, and provides similar recovery term
structures for different functional specifications. Given that the model is easy to un-
derstand and calibrate, it may be used to further the development of credit derivatives
indexed to recovery rates, such as recovery swaps and digital default swaps, as well as
provide recovery rate inputs for the implementation of Basel II.
JEL Codes: G0, G1.
∗Thanks to the editor Carl Chiarella, an Associate Editor, and two anonymous referees for very useful
guidance on the paper. We are grateful to Viral Acharya, Santhosh Bandreddi, Christophe Barat, Darrell
Duffie, Lisa Goldberg, Francis Longstaff and Raghu Sundaram, as well as seminar participants at Barclays
Global Investors, Moodys KMV, Standard & Poors, University of Chicago’s Center for Financial Math-
ematics, and the American Mathematical Society Meetings 2008, who gave us many detailed and useful
suggestions. We are grateful to RiskMetrics for the data. The first author received the financial support of
a Santa Clara University grant and a Breetwor fellowship. The authors may be contacted at: Sanjiv Das,
Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, Email: srdas@scu.edu. Paul Hanouna,
Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, Email: paul.hanouna@villanova.edu.
1