18.2 internal ratings based approach

Copyright © 2018 CapitaLogic Limited
This presentation file is prepared in accordance with
Chapter 18 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
Chapter 18
Internal Ratings
Based Approach

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.

Outline
 Theory of the IRB approach
 Retail IRB approach
 Advanced IRB approach
 Foundation IRB approach
 Implementation of the IRB approach

The IRB theory
 A bank holds a well diversified debt portfolio
 A large number of debts
 Smaller EAD
 Many debt issuers
 RMs unified to 1 year
Portfolio XCL = Portfolio EAD × LGD × XCDR
Portfolio 1-year EL = Portfolio EAD × LGD × PD
Portfolio UL = Portfolio XCL - Portfolio 1-year EL

Single debt UL
 For each debt k, define
 A total of NOB debts
k k k k
k k k k
k k k
1-year EL = EAD × LGD × PD
XCL =
UL
EAD × LGD ×
= XCL -
X DR
EL
C
NOB
k
k=1
EAD = Portfolio EAD
k
k
k
LGD LGD
XCDR XCDR
PD PD




Portfolio UL
 
NOB NOB
k k
k=1 k=1
NOB
k
k=1
Portfolio UL = Portfolio XCL - Portfolio 1-year EL
= Portfolio EAD × LGD × XCDR - Portfolio EAD × LGD × PD
= EAD × LGD × XCDR - EAD × LGD × PD
= EAD × LGD × XCDR - EAD
   
   
   
 
  
   
 
NOB
k
k=1
NOB NOB
k k k k k k
k=1 k=1
NOB
k k
k=1
NOB
k
k=1
× LGD × PD
EAD × LGD × XCDR - EAD × LGD × PD
= XCL - 1-year EL
= UL


 



Exposure at default
 On balance sheet debt
 Term loan, mortgage, bond
 EAD = Principal + Accrued Interest
 Commitment
 A promise to lend up to a certain amount
 Credit card, card line
 EAD = Drawdown amount
+ (Credit limit - Drawdown amount) × CCF
 CCF estimated by bank’s internal model

Loss given default
 Estimated by
 Bank’s internal quantitative model
 Taking into account collaterals
 Particularly important for residential
mortgage
 When property value goes up continuously
 LGD = 0 => Default loss = 0
 LGD floor is set artificially to 10%

Probability of default
 Estimated by
 Bank’s internal ratings system
 PD floor
 Minimum 0.03% except for a country which has
sole discretion on its currency policy

Residual maturity
 Effective RM
 Expected cash flow weighted RM; or
 Contractual maturity
 RM floor one year
 RM cap five years  
N
k k
k=1
N
k
k=1
CF × Tenor
RM =
CF


Example 18.1

IRB formulas by exposure
IRB approach
Retail IRB
Residential mortgage
Other retail exposure
A-IRB and F-IRB
SME corporate
exposure
Large financial
institution exposure
Institution exposure
Qualifying revolving
retail exposure

Outline
 Implementation of the IRB

Retail exposures
 Retail
 Individual person
 Small business
 with annual revenue < EUR 5 mn
 lending from a bank < EUR 1 mn
 Managed and calculated on a pool basis
 A large finite homogenous portfolio
 At least 300 debt issuers per pool
 EAD, LGD and PD estimated for each pool

A pool of residential mortgages
Example 18.2
   -1 -1
CCC = 0.15
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
XCL = EAD × LGD × XCDR
UL = XCL - 1-year EL
CP = 1-year EL
CC = 1.06UL
 
 
  

A pool of
qualifying revolving retail exposures
Example 18.3
   -1 -1
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
CP = 1-y
CCC =
ear EL
CC = 1.06UL
0.04
 
 
  

A pool of other retail exposures
Example 18.4
 
   -1 -1
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
UL = XCL - 1-
CCC = 0.03 + 0.
year EL
CP = 1-year EL
CC = 1.06
13exp -3
U
5PD
L
 
 
  

Outline

Institution exposure
Example 18.5
 
 
2
b = 0.11852 - 0.05478ln PD
1 + RM -
CP = 1-yea
2.5 b
M
r
AF =
1
EL
CC = 1.06UL ×
- 1.5b
MAF
  
 
   -1 -1
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
1-year EL = E
C
A
CC = 0.12 1
D × LGD ×
+ exp -
PD
50PD  
 
 
  

SME corporate exposure
Example 18.6
 
 
2
b = 0.11852 - 0.05478ln PD
1 + RM - 2.5 b
MAF =
1 - 1.5b
CP = 1-year EL
CC = 1.06UL × MAF
  
 
   -1 -1
CCC = 0.12 1 + exp -50PD
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
1-year EL = EAD
S - 5
× LGD × PD
UL = XCL - 1-y
0
+
112
ear EL
5
  
 
 
  
For a SME with total annual
revenue < EUR 50 mn
S: Total annual revenue in EUR mn

Large financial institution exposure
Example 18.7
 
 
2
b = 0.11852 - 0.05478ln PD
1 + RM - 2.5 b
MAF =
1 - 1.5b
CP = 1-year EL
CC = 1.06UL × MAF
  
 
   -1 -1
CCC = 1 + exp -50PD
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
UL = XCL - 1-year
0.15
EL
  
 
 
  
For a financial institution with
total assets > USD 100 bn

Credit risk mitigation
 Reduction of EAD
 On balance sheet netting
 Reduction of LGD
 Collaterals
 Reduction of PD
 Default insurance
 Credit guarantee
 CDS

On balance sheet netting
 Bilateral netting agreement in place
 
Net EAD
Lending EAD
= Max - Borrowing EAD 1 - Currency haircut ,
0
 
 
 
 
 

Default insurance
 Credit guarantor/protection independent of debt
issuer
 Substitution framework
 For both retail and advanced IRB approaches
 Credit guarantor/protection seller with higher credit
quality
 PD of credit guarantor/protection seller adopted in the
calculations of CP and CC
 Double default framework
 For advanced IRB approach only
 CP and CC calculated by double default IRB formulas
Example 18.8

Double default framework
Example 18.9
  
 
o g
g
2
b = 0.11852 - 0.05478ln
1 + RM - 2.5 b
Min PD , PD
DDF = 0.15 + 160PD
CP
MAF =
1 - 1.5b
CC = 1.06UL × MAF
= 0
DDF×
 
 
 
 
 
   
o
o
o
-1 -1
o
o
CCC = 0.12 1 + exp -50PD or
S - 50
CCC = 0.12 1 + exp -50PD + or
1125
CCC = 0.15 1 + exp -50PD
Φ PD + Φ 99.9% CCC
XCDR = Φ
1 - CCC
UL = XC
  
  
  
 
 
  
L - 1-year EL

Currency and maturity mis-matches
 Currency mis-match
 Protected part reduced by 8%
 Maturity mis-match
 Protected part reduced to
 RM > 0.25
 RM < 0.25
 Credit risk control ignored simply
 
 
EAD of the protected part without maturity mis-match
Min Protection period of credit risk control, 5 - 0.25
×
Min RM of debt, 5 - 0.25
Example 18.10
Example 18.11

Outline

Exposure at default
Type of commitment CCF (%)
1. Direct credit substitutes 100
2. Transaction related contingencies 50
3. Trade related contingencies 20
4. Asset sales with recourse 100
5. Forward asset purchases 100
6. Partly paid-up securities 100
7. Forward forward deposits placed 100
8. Note issuance and revolving underwriting facilities 75
9. Commitments that are unconditionally cancellable without prior notice 0
10. Other commitments 75*
* Different from the standardized approach

Loss given default
 45% for senior debt
 75% for subordinated debt
 Recognized collaterals
 Financial collaterals in standardized approach
 IRB collaterals
 Financial receivables
 Real estate
 Physical assets

Financial collaterals
Collateral and
credit rating
Constituent /
residual maturity
Corporation
and bank (%)
Country (%)
Debt
AAA and
AA
Up to 1 year 1 0.5
From 1 to 5 years 4 2
Longer than 5 years 8 4
A and BBB
Up to 1 year 2 1
From 1 to 5 years 6 3
Longer than 5 years 12 6
BB 15
Equity of a listed
company
Constituent of a major
equity index
15
Not a constituent of
major equity indices
25
Others 100
Mutual fund The largest haircut among the investment components

Senior debt with financial collaterals
EAD - Collateral value
1 - Collateral haircut
Max ×
- Currency haircut
0
LGD = 45% ×
EAD
 
 
  
   
 
  

IRB collaterals
Lower bound
C* (%)
Upper bound
C** (%)
Collateral
LGD (%)
Financial
receivables 0 125 35
Real estate 30 140 35
Physical assets 30 140 40

Senior debt subject to IRB collaterals
*
**
** **
Collateral value
C =
EAD
45% C less than C
LGD = Collateral LGD C greater than C
C C
45% × 1 - + Collateral LGD × C in between
C C
 
 
 

Probability of default
and residual maturity
 PD
 Following the advanced IRB approach
 RM
 2.5 years; or
 Following the advanced IRB approach, subject to
regulatory approval

Outline
 Implementation of the IRB approach

Capital charge
calculation approaches
Sophist
-ication
Approach
Internal
model
Regulatory
rule
High
Retail IRB*
Advanced
IRB
EAD, LGD,
PD, RM
Medium
Foundation
IRB
PD, RM EAD, LGD
PD
EAD, LGD,
RM
Low Standardized EAD, CCR
* RM not applicable

Benefits of the IRB approach
 Savings on regulatory capital
 Less capital charge for debts of higher credit
quality
 Material savings on retail lending
 An exhibition of advanced credit risk
management expertise

Comparison: capital charge ratio
Exposure LGD (%) RM (yr) Approach AA (%) A (%) BBB (%) BB (%) B (%)
Retail 90
IRB 0.82 1.66 4.32 10.38 11.79
Standardized 6 6 6 6 6
Institute
45 1
IRB 0.70 1.39 3.52 8.43 12.95
Standardized 1.6 4 4 8 8
75 1
IRB 1.16 2.32 5.86 14.73 21.58
Standardized 1.6 4 4 8 8
Example 18.12, 18.13, 18.14

Internal ratings system
 A consolidated opinion from
 PD derived from quantitative model
 Agency credit rating
 Specialist judgment
 Internal rating => average PD
 7-level
 AAA, AA, A, BBB, BB, B, C
 19-level
 AAA, AA (+/-), A (+/-), BBB (+/-),
BB (+/-), B (+/-), CCC, CC, C

IRB system
Credit data Rating systems Capital
charge engine
Regulatory reports
EAD, LGD,
PD, RM
CP, CC

Capital charge engine

18.2 internal ratings based approach

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