Regulatory IRB Validation Techniques

Copyright © 2018 CapitaLogic Limited
Chapter 19
Regulatory
IRB Validation
This presentation file is prepared in accordance with
Chapter 19 of the text book
“Managing Credit Risk Under The Basel III Framework, 3rd ed”
Website : https://sites.google.com/site/crmbasel
E-mail : crmbasel@gmail.com

Copyright © 2018 CapitaLogic Limited 2
Declaration
 Copyright © 2018 CapitaLogic Limited.
 All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
 Authored by Dr. LAM Yat-fai (林日辉),
Director, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.

Model validation
 Hypothesis testing
H0: Empirical price - Model price = 0
Ha: Empirical price - Model price ≠ 0
 1,000 samples
 90th percentile confidence interval
 If the p-value < 1 - confidence interval,
reject the null hypothesis

Characteristics of the PD models
 There is a lack of default records due to many
banks’ conservative lending practices
 Empirical default is a binary process which
cannot be used directly to validate a PD
having any value between 0 and 1
 The empirical CCC is unobservable

Principles of
regulatory IRB validation
 A bank has the primary responsibility for the regulatory IRB
validation
 Regulatory IRB validation is fundamentally about assessing
the predictive ability of a bank’s risk estimates and the use of
ratings in credit processes
 There is no single method of regulatory IRB validation
 The regulatory IRB validation is an iterative process
 The regulatory IRB validation should encompass both
quantitative and qualitative elements
 The regulatory IRB validation processes and outcomes should
be subject to independent review

The IRB validation
 Board and senior
management oversight
 Transparency
 Accountability
 Independence
 Data quality
 Use test
 Benchmarking
 Frequency
 Internal and external
audit functions
 Stress testing
 Quantitative
requirements
 PD validation
 External vendor
models

Board of Directors and
senior management oversight
 Board of Directors
 General understanding of the regulatory requirements on
the IRB approach
 Approval of the critical elements of the IRB systems
 Establishing an effective Basel III project management
framework
 Senior management
 Development of policies and procedures
 Allocation of resources
 Responsible for the day-to-day operations

Transparency
 Third parties’ understanding of the design,
operations and accuracy of a bank’s IRB
systems
 Delivered primarily through documentation
 More overrides with human judgment, less
transparency

Accountability
 Policies in place to identify functions
responsible for rating accuracy and rating
system performance
 Measurable performance standards for staff
with incentive compensation tied to these
standards
 Chief Credit Risk Officer to bear the
responsibility for the overall performance of
the IRB systems

Independency
 The IRB implementation team independent of
sales and marketing
 The IRB review team independent of the IRB
implementation team
 To ensure objectivity and accuracy
 Use of external experts to enhance the
independency

Data quality
 Difficult to maintain due to the large amount
of data in a bank
 Reconciliation between the IRB and finance
data
 Independent assessment of data quality at
least annually

Use test
 The internal ratings and default loss estimates
must play an essential role in the credit
approval, risk management, capital allocation
and corporate governance functions
 For the first few years: credit approval, credit
monitoring and reporting of credit risk
information to the Board and senior
management

Benchmarking
 Benchmarks obtained from third parties, e.g.
credit rating agencies and/or credit bureau
 Consistent with the benchmark?
 Why inconsistent with the benchmark?
 Benchmarks may not be available

Frequency
 At least annual
 Start in 12 months
 Complete in 18 months
 Different IRB systems to be validated in
different time periods

Internal and external audit functions
 The most independent reviewer
 Internal audit function
 For larger banks
 External audit function
 For smaller banks lacking expertise
 For larger banks to demonstrate further
independency

Stress testing
 To exhibit the impact to a bank under extreme
scenarios, e.g.
 Collateral values decreased by 50%
 All borrowers downgraded
 CDSs cannot be entered for protection

Quantitative requirements
 No universal standard
 Difficult due to limited default records
 Different for PD and LGD
 PD validation the most important

PD validation (1)
 To validate the discriminatory power of the PD
 Cumulative accuracy profile and Gini coefficient
 Receiver operating characteristic, receiver operating
characteristic measure & Pietra Index
 Bayesian error rate
 Entropy measures
 Information value
 Kendall’s Tau and Somers’ D
 Brier score
 Divergence

PD validation (2)
 To validate the calibration of an internal
rating system
 Binomial test with assumption of zero CCC
 Binomial test with assumption of non-zero CCC
calculated by one of the six CCC formulas
 Goodness of fit for rating scale
 To assess whether a model is UNRELIABLE

Copyright 2016 CapitaLogic Limited 20
No. of default tests (assuming
independent default dependency)
 Hypothesis
 H0: Actual no. of defaults follows those estimated
by the PD
 Ha: Actual no. of defaults does not those
estimated by the PD
 Confidence level
 95th percentile
 p-value < 5% to reject the null hypothesis
 Binomial distribution
Example 19.1

Binomial distribution
 Probability mass function
 Cumulative mass function
 
 
 
 
NOB-kk
NOB k
M
NOB-kk
NOB k
k=0
Probability k defaults out of NOB borrowers
= C × PD × 1 - PD
Probablity Up to M defaults out of NOB borrowers
= C × PD × 1 - PD 
 

No. of default tests (assuming
Basel III CCC structure)
 Hypothesis
 H0: Actual no. of defaults follows those estimated
by the PD
 Ha: Actual no. of defaults does not those
estimated by the PD
 95th percentile
 Vasicek default rate distribution Example 19.2

Vasicek default rate distribution
 
     
 
     
   
22 -1 -1-1
2
-1 -1-1
DR
0
-1 -1
1 - CCC Φ DR - Φ PDΦ DR1 - CCC
f DR = exp -
CCC 2 2CCC
Φ PD - 1 - CCC Φ τΦ τ1 - CCC
F DR = exp - dτ
CCC 2 2CCC
1 - CCC Φ DR - Φ PD
= Φ
CCC
       
 
 
 
    
 
 
 
 
 
  

 Probability density function
 Cumulative probability distribution function

Basel III ECAI Plus rating scale
Credit quality Rating 3-year DR (%) PD (%)
Excellent AAA 0.03 0.0100
Good
AA (+,-) 0.10 0.0333
A (+,-) 0.25 0.0834
BBB (+,-) 1.00 0.3345
Moderate
BB (+,-) 7.50 2.5652
B (+,-) 20.00 7.1682
Bad
CCC 40.00 15.6567
CC 65.00 29.5270
C 95.00 63.1597

Goodness of fit test for rating scale
 Hypothesis
 H0: Actual nos. of defaults follows those
estimated by the rating scale
 Ha: Actual nos. of defaults does not those
estimated by the rating scale
 95th percentile
 Chi-squared statistic

Chi-squared statistic
 Chi-squared distribution

 p-value
 1 - CHITEST(Actual, Estmiated)
 
k
- 1
2
k
2
x
x exp -
2
f x, k = x 0
k
2 Γ
2
 
  
  
 
  
 
Example 19.3

In sample test vs out sample test
 In sample test
 Model derived from one data set
 Validation also conducted on the same data set
 A test of internal consistency
 Out sample test
 Model derived from one data set
 Validation conducted on another data set
 A test of model stability

External vendor models
 An outsourcing activity
 Transparency
 Documentation
 Skill transfer

Regulatory IRB Validation Techniques

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