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. 2009-10
How Well Does the Vasicek-Basel AIRB Model Fit the Data?
Evidence from a Long Time Series of Corporate Credit Rating Data
November 2009
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. 2009-10
How Well Does the Vasicek-Basel AIRB Model Fit the Data?
Evidence from a Long Time Series of Corporate Credit Rating Data
November 2009
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
1
How Well Does the Vasicek-Basel AIRB Model Fit the Data?
Evidence from a Long Time Series of Corporate Credit Rating
Data
by
Paul H. Kupiec∗
November 2009
ABSTRACT
I develop methods that produce consistent estimates of the Vasicek-Basel IRB (VAIRB)
credit risk model parameters. I apply these methods to Moody’s data on corporate
defaults over the period 1920–2008 and assess the model fit and construct hypothesis
tests using bootstrap methods. The results show that the VAIRB does not capture the
variability in Moody’s default data: there are numerous episodes in which obligors
default with much greater frequency than predicted. This pattern is consistent with a
missing common factor that affects default correlation only intermittently—a missing
factor similar to the frailty covariate in Duffie et al. (2009). Unlike Lopez (2004), I find
the VAIRB correlation parameter to be larger for lower-rated credits. I use estimates of
the VAIRB error distribution to construct capital allocations for model risk and find that
the capital buffers for model risk are substantial, especially for lower-graded credits.
VAIRB common factor estimates exhibit positive autocorrelation and thus long time
series are usually necessary to produce reliable model estimates. Alternatively, I use
common factor and correlation parameter estimates from the 1920-2008 data to control
for common factor realizations when estimating unconditional default rates (PDs) from
short samples. I estimate PDs and confidence intervals using default data for Moody’s
alpha-numeric rating grades (1998-2008). After correcting for common factor effects,
sample average default rates are shown to overstate the PD for most credit grades in this
sample period.
∗ Federal Deposit Insurance Corporation. The views expressed are my own and do not
necessarily reflect the views of the FDIC. For comments on a preliminary draft of this
paper, I am grateful to Bob Jarrow, Ed Kane, Matt Pritsker, members of the Basel
Implementation Validation Subgroup; participants in seminars at the Federal Reserve
Bank of Richmond and the Federal Reserve Bank of Cleveland, and discussions at the
Federal Reserve Bank of San Francisco January 2009 Conference on Financial Markets,
the interagency quantitative risk modeling workshop held at the Federal Reserve Bank of
Philadelphia, and the September 2009 Bocconi University CAREFIN conference.
E-mail: pkupiec@fdic.gov.
How Well Does the Vasicek-Basel AIRB Model Fit the Data?
Evidence from a Long Time Series of Corporate Credit Rating
Data
by
Paul H. Kupiec∗
November 2009
ABSTRACT
I develop methods that produce consistent estimates of the Vasicek-Basel IRB (VAIRB)
credit risk model parameters. I apply these methods to Moody’s data on corporate
defaults over the period 1920–2008 and assess the model fit and construct hypothesis
tests using bootstrap methods. The results show that the VAIRB does not capture the
variability in Moody’s default data: there are numerous episodes in which obligors
default with much greater frequency than predicted. This pattern is consistent with a
missing common factor that affects default correlation only intermittently—a missing
factor similar to the frailty covariate in Duffie et al. (2009). Unlike Lopez (2004), I find
the VAIRB correlation parameter to be larger for lower-rated credits. I use estimates of
the VAIRB error distribution to construct capital allocations for model risk and find that
the capital buffers for model risk are substantial, especially for lower-graded credits.
VAIRB common factor estimates exhibit positive autocorrelation and thus long time
series are usually necessary to produce reliable model estimates. Alternatively, I use
common factor and correlation parameter estimates from the 1920-2008 data to control
for common factor realizations when estimating unconditional default rates (PDs) from
short samples. I estimate PDs and confidence intervals using default data for Moody’s
alpha-numeric rating grades (1998-2008). After correcting for common factor effects,
sample average default rates are shown to overstate the PD for most credit grades in this
sample period.
∗ Federal Deposit Insurance Corporation. The views expressed are my own and do not
necessarily reflect the views of the FDIC. For comments on a preliminary draft of this
paper, I am grateful to Bob Jarrow, Ed Kane, Matt Pritsker, members of the Basel
Implementation Validation Subgroup; participants in seminars at the Federal Reserve
Bank of Richmond and the Federal Reserve Bank of Cleveland, and discussions at the
Federal Reserve Bank of San Francisco January 2009 Conference on Financial Markets,
the interagency quantitative risk modeling workshop held at the Federal Reserve Bank of
Philadelphia, and the September 2009 Bocconi University CAREFIN conference.
E-mail: pkupiec@fdic.gov.