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. 2007-06
A Generalized Single Common Factor Model of Portfolio Credit Risk
June 2007
Empirical Comparisons and Implied Recovery Rates
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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. 2007-06
A Generalized Single Common Factor Model of Portfolio Credit Risk
June 2007
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
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A Generalized Single Common Factor Model of Portfolio
Credit Risk
by
Paul H. Kupiec
June 2007
ABSTRACT
The Vasicek single factor model of portfolio credit loss is generalized to include credits with
stochastic exposures (EADs) and loss rates (LGDs). The model can accommodate any
distribution and correlation assumptions for the LGDs and EADs and will produce a closed-
form expression for an asymptotic portfolio’s conditional loss rate. Revolving exposures
draw against committed lines of credit. Dependence among defaults, EADs, and LGDs are
modeled using a single common Gaussian factor. A closed-form expression for an
asymptotic portfolio’s inverse cumulative conditional loss rate is analyzed for alternative
EAD and LGD assumptions. Positive correlation in individual credits’ EAD and LGD
realizations increases portfolio systematic risk, producing wider ranges and increased
skewness in portfolio loss distributions.
Division of Insurance and Research, Federal Deposit Insurance Corporation. The views
expressed are those of the author and do not reflect the views of the FDIC. I am grateful to
Rosalind Bennett, Steve Burton, Sanjiv Das, Jin-Chuan Duan, Greg Gupton, Robert Jarrow,
Peter Raupach, and Stuart Turnbull for helpful comments on an earlier draft of this paper. E-
mail: pkupiec@fdic.gov.
Credit Risk
by
Paul H. Kupiec
June 2007
ABSTRACT
The Vasicek single factor model of portfolio credit loss is generalized to include credits with
stochastic exposures (EADs) and loss rates (LGDs). The model can accommodate any
distribution and correlation assumptions for the LGDs and EADs and will produce a closed-
form expression for an asymptotic portfolio’s conditional loss rate. Revolving exposures
draw against committed lines of credit. Dependence among defaults, EADs, and LGDs are
modeled using a single common Gaussian factor. A closed-form expression for an
asymptotic portfolio’s inverse cumulative conditional loss rate is analyzed for alternative
EAD and LGD assumptions. Positive correlation in individual credits’ EAD and LGD
realizations increases portfolio systematic risk, producing wider ranges and increased
skewness in portfolio loss distributions.
Division of Insurance and Research, Federal Deposit Insurance Corporation. The views
expressed are those of the author and do not reflect the views of the FDIC. I am grateful to
Rosalind Bennett, Steve Burton, Sanjiv Das, Jin-Chuan Duan, Greg Gupton, Robert Jarrow,
Peter Raupach, and Stuart Turnbull for helpful comments on an earlier draft of this paper. E-
mail: pkupiec@fdic.gov.