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Similar to Chapter 18 internal ratings based approach
Similar to Chapter 18 internal ratings based approach (20)
Chapter 18 internal ratings based approach
- 1. Copyright © 2017 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
- 2. Copyright © 2017 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),
Principal, Structured Products Analytics, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.
- 3. Copyright © 2017 CapitaLogic Limited 3
Outline
Theory of the IRB approach
Retail IRB approach
Advanced IRB approach
Foundation IRB approach
Implementation of the IRB approach
- 4. Copyright © 2017 CapitaLogic Limited 4
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 WCL = Portfolio EAD × LGD × WCDR
Portfolio 1-year EL = Portfolio EAD × LGD × PD
Portfolio UL = Portfolio WCL - Portfolio 1-year EL
- 5. Copyright © 2017 CapitaLogic Limited 5
Single debt UL
For each debt k, define
A total of N debts
k k k k
k k k k
k k k
1-year EL = EAD × LGD × PD
WCL =
UL
EAD × LGD ×
= WCL -
W DR
EL
C
N
k
k=1
EAD = Portfolio EAD
k
k
k
LGD LGD
WCDR WCDR
PD PD
- 6. Copyright © 2017 CapitaLogic Limited 6
Portfolio UL
N N
k k
k=1 k=1
N
k k
k=1
Portfolio UL = Portfolio WCL - Portfolio 1-year EL
= Portfolio EAD × LGD × WCDR - Portfolio EAD × LGD × PD
= EAD × LGD × WCDR - EAD × LGD × PD
= EAD × LGD × WCDR - EAD × LG
N
k=1
N N
k k k k k k
k=1 k=1
N
k k
k=1
N
k
k=1
D × PD
EAD × LGD × WCDR - EAD × LGD × PD
= WCL - 1-year EL
= UL
- 7. Copyright © 2017 CapitaLogic Limited 7
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
- 8. Copyright © 2017 CapitaLogic Limited 8
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%
- 9. Copyright © 2017 CapitaLogic Limited 9
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
- 10. Copyright © 2017 CapitaLogic Limited 10
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
- 11. Copyright © 2017 CapitaLogic Limited 11
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
- 12. Copyright © 2017 CapitaLogic Limited 12
Outline
Theory of the IRB approach
Retail IRB approach
Advanced IRB approach
Foundation IRB approach
Implementation of the IRB
- 13. Copyright © 2017 CapitaLogic Limited 13
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
- 14. Copyright © 2017 CapitaLogic Limited 14
A pool of residential mortgages
Example 18.2
-1 -1
CCC = 0.15
Φ PD + Φ 99.9% CCC
WCDR = Φ
1 - CCC
WCL = EAD × LGD × WCDR
1-year EL = EAD × LGD × PD
UL = WCL - 1-year EL
CP = 1-year EL
CC = 1.06UL
- 15. Copyright © 2017 CapitaLogic Limited 15
A pool of
qualifying revolving retail exposures
Example 18.3
-1 -1
Φ PD + Φ 99.9% CCC
WCDR = Φ
1 - CCC
WCL = EAD × LGD × WCDR
1-year EL = EAD × LGD × PD
UL = WCL - 1-year EL
CP = 1-y
CCC =
ear EL
CC = 1.06UL
0.04
- 16. Copyright © 2017 CapitaLogic Limited 16
A pool of other retail exposures
Example 18.4
-1 -1
Φ PD + Φ 99.9% CCC
WCDR = Φ
1 - CCC
WCL = EAD × LGD × WCDR
1-year EL = EAD ×
1 - exp -35PD
CCC = 0.16 -
LGD × PD
UL = WCL - 1-ye
0.13
ar EL
CP = 1-year EL
CC =
1 - exp -35
1.06UL
- 17. Copyright © 2017 CapitaLogic Limited 17
Outline
Theory of the IRB approach
Retail IRB approach
Advanced IRB approach
Foundation IRB approach
Implementation of the IRB
- 18. Copyright © 2017 CapitaLogic Limited 18
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
WCDR = Φ
1 - CCC
WCL = EAD × LG
1 - exp -50PD
CCC = 0.24 - 0.12
1 -
D × WCDR
1-year EL = EAD × LGD ×
ex
PD
UL = WCL - 1-year EL
p -50
- 19. Copyright © 2017 CapitaLogic Limited 19
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
1 - exp -50PD
CCC = 0.24 - 0.12
1 - exp -50
Φ PD + Φ 99.9% CCC
WCDR = Φ
1 - CCC
WCL = EAD × LGD × WCDR
1-year EL = EAD × L
S - 50
+
112
GD × PD
UL = WCL - 1-year EL
5
For a SME with total annual
revenue < EUR 50 mn
S: Total annual revenue in EUR mn
- 20. Copyright © 2017 CapitaLogic Limited 20
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
1 - exp -50PD
CCC = 0.24 - 0.12
1 - exp -50
Φ PD + Φ 99.9% CCC
WCDR = Φ
1 - CCC
WCL = EAD × LGD × WCDR
1-year EL = EAD × LGD × PD
UL = WCL - 1-ye
1.25
ar EL
For a financial institution with
total assets > USD 100 bn
- 21. Copyright © 2017 CapitaLogic Limited 21
Credit risk mitigation
Reduction of EAD
On balance sheet netting
Reduction of LGD
Collaterals
Reduction of PD
Default insurance
Credit guarantee
CDS
- 22. Copyright © 2017 CapitaLogic Limited 22
On balance sheet netting
Bilateral netting agreement in place
Net EAD
Lending EAD
= Max - Borrowing EAD 1 - Curreny haircut ,
0
- 23. Copyright © 2017 CapitaLogic Limited 23
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
- 24. Copyright © 2017 CapitaLogic Limited 24
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
1 - exp -50PD
CCC = 0.24 - 0.12 or
1 - exp -50
1 - exp -50PD S - 50
CCC = 0.24 - 0.12 + or
1 - exp -50 1125
1 - exp -50PD
CCC = 1.25 0.24 - 0.12
1 - exp -50
Φ PD + Φ 99
WCDR = Φ
o
.9% CCC
1 - CCC
WCL = EAD × LGD × WCDR
1-year EL = EAD × LGD × PD
UL = WCL - 1-year EL
- 25. Copyright © 2017 CapitaLogic Limited 25
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
No default protection
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
- 26. Copyright © 2017 CapitaLogic Limited 26
Outline
Theory of the IRB approach
Retail IRB approach
Advanced IRB approach
Foundation IRB approach
Implementation of the IRB
- 27. Copyright © 2017 CapitaLogic Limited 27
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.
- 28. Copyright © 2017 CapitaLogic Limited 28
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
- 29. Copyright © 2017 CapitaLogic Limited 29
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
- 30. Copyright © 2017 CapitaLogic Limited 30
Senior debt with financial collaterals
EAD - Collateral value
1 - Collateral haircut
Max ×
- Currency haircut
0
LGD = 45% ×
EAD
- 31. Copyright © 2017 CapitaLogic Limited 31
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
- 32. Copyright © 2017 CapitaLogic Limited 32
Senior debt subject to IRB collaterals
*
**
** **
Collateral value
C =
EAD
45% C is less than C
LGD = Collateral LGD C is greater than C
C C
45% × 1 - + Collateral LGD × C is in between
C C
- 33. Copyright © 2017 CapitaLogic Limited 33
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
- 34. Copyright © 2017 CapitaLogic Limited 34
Outline
Theory of the IRB approach
Retail IRB approach
Advanced IRB approach
Foundation IRB approach
Implementation of the IRB approach
- 35. Copyright © 2017 CapitaLogic Limited 35
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
- 36. Copyright © 2017 CapitaLogic Limited 36
Benefits of the IRB approach
Savings on regulatory capital
Less capital charge for debt of higher credit
quality
Material savings on retail lending
An exhibition of advanced credit risk
management expertise
- 37. Copyright © 2017 CapitaLogic Limited 37
Comparison: capital charge ratio
Exposure LGD (%) RM (yr) Approach AA (%) A (%) BBB (%) BB (%) B (%)
Retail 60
IRB 0.55 1.10 5.20 6.92 7.86
Standardized 6 6 6 6 6
Institute
45 3
IRB 1.51 2.55 8.40 10.96 14.95
Standardized 1.6 4 4 8 8
75 3
IRB 2.51 4.25 13.99 18.27 24.91
Standardized 1.6 4 4 8 8
Example 18.12, 18.13, 18.14
- 38. Copyright © 2017 CapitaLogic Limited 38
Internal ratings system
A consolidated opinion from
PD derived from quantitative model
Agency credit rating
Specialist judgment
Internal rating => average PD
7-grade
AAA, AA, A, BBB, BB, B, C
19-grade
AAA, AA (+/-), A (+/-), BBB (+/-),
BB (+/-), B (+/-), CCC, CC, C
- 39. Copyright © 2017 CapitaLogic Limited 39
IRB system
Credit data Rating systems Capital
charge engine
Regulatory reports
EAD, LGD,
PD, RM
CP, CC