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Specialized Lending Rating Model using AHP
Credit Risk Modelling
Edinburgh, 28th August 2013.
Specialized lending Specialized lending
AHP methodology AHP methodology
IPRE model IPRE model
Validation Validation Conclusion Conclusion
Agenda
2
Specialized lending
Specialized lending - 4 subclasses:
Income Producing Real Estate (IPRE)
Project Finance
Object Finance
Commodities Finance
Basel Commitee approaches:
Standardized approach
Foundation IRB
Advanced IRB
Slotting approach (only for specialized lending)
3
AHP METHODOLOGY
Credit Risk Modelling
Edinburgh, 28th August 2013.
Analytical hierarchy process (methodology overview)
Introduced by Thomas L. Saaty
Hierarchical structure – goal on top, criteria and subcriteria in the middle,
options on bottom (example of one criteria and one subcriteria level):
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GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
Analytical hierarchy process (1st step)
For each subcriteria construct pairwise comparison matrices and
corresponding priority vector:
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GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
1 a12 a13
1/a12 1 a23
1/a13 1/a23 1
3×3
Option1 Option2 Option3
Option1
Option2
Option3
normalization
calculation
of eigen vector
& eigen value
x1
y1
z1
Option1
Option2
Option3
3×1
x1+y1+z 1= 1
e.g. SC1: e.g. SC1:
Intensity of
Importance Definition
1 Equal importance
2 Weak or slight
3 Moderate importance
4 Moderate plus
5 Strong importance
6 Strong plus
7 Very strong or demonstrated importance
8 Very, very strong
9 Extreme importance
Pairwise comparison
How is pairwise comparison conducted? Using scale (1-9):
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Construct positive reciprocal matrix:
nnnn
ijii
nj
nj
aaa
aaa
aaaa
aaaa
21
21
222221
111211
where:
a11 = a22 = ... = ann = 1,
aji = aij-1
where:
a11 = a22 = ... = ann = 1,
aji = aij-1
Consistency index and consistency ratio
How to check whether the weights in comparison matrix consistent? We
calculate eigenvalues of comparison matrices:
Condition for perfectly consistent weights: aik = aijajk
Condition for perfectly consistent matrices: λmax = n
Consistency index:
Consistency ratio:
• CR ≤ 0,1 → acceptable inconsistency
Random consistency index (RI) by Saaty:
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n 1 2 3 4 5 6 7 8 9 10
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49
Analytical hierarchy process (2nd step)
For each subcriteria group construct matrices out of eigen vectors:
9
GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
x1
y1
z1
3×1
x2
y2
z2
x1 x2
y1 y2
z1 z2
3×2 x3
y3
z3
3×1
x4
y4
z4
x3 x4
y3 y4
z3 z4
3×2 x5
y5
z5
3×1
x6
y6
z6
x5 x6
y5 y6
z5 z6
3×2
Analytical hierarchy process (3rd step)
For each criterion construct pairwise comparison matrix and
corresponding priority vector:
10
GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
1 b12
1/b12 1
2×2 e.g. C1: e.g. C1:
SC1 SC2
SC1
SC2
normalization
calculation
of eigen vector
& eigen value
i1
j1
SC1
SC2
2×1
i1+j1= 1
Analytical hierarchy process (4th step)
For each criteria calculate priority vector:
11
GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
x1 x2
y1 y2
z1 z2
3×2
x3 x4
y3 y4
z3 z4
3×2
x5 x6
y5 y6
z5 z6
3×2
× i1
j1
=
2×1
× i2
j2
=
2×1 k1
m1
n1
3×1
k2
m2
n2
3×1
× i3
j3
=
2×1 k3
m3
n3
3×1
Analytical hierarchy process (5th step)
Construct matrix out of eigen vectors and construct pairwise
comparison matrix,corresponding priority vector and eigen value:
12
GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
k1
m1
n1
3×1
k2
m2
n2
3×1
k3
m3
n3
3×1
k1 k2 k3
m1 m2 m3
n1 n2 n3
3×3
1 c12 c13
1/c12 1 c23
1/c13 1/c23 1
3×3
C1 C2
C1
C2
normalization
calculation
of eigen vector
& eigen value
C1
C2
3×1
∑= 1
C3
C3
d
f
g C3
Option2
Analytical hierarchy process (final step)
Calculate final priority vector on which decision will be made:
13
GOAL GOAL
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
OPTION1 OPTION1 OPTION2 OPTION2 OPTION3 OPTION3
k1 k2 k3
m1 m2 m3
n1 n2 n3
3×3 3×1
d
f
g
× =
3×1
q
r
t
max {q,r,t} choice choice
Option1
Option3
IPRE MODEL
Credit Risk Modelling
Edinburgh, 28th August 2013.
Model segmentation
Four sub models:
1) Constructed real estate for sale
2) Real estate under construction for sale
3) Constructed real estate for lease
4) Real estate under construction for lease
Five top level criteria common to all four sub models:
1) Financial strength
2) Political and legal environment
3) Project and/or asset characteristics
4) Strength of the sponsor and developer
5) Security package
Subcriteria and their weights differ across sub models
15
Model overview
Example of rating criteria for one of the submodels:
16
Rating
Financial strength
Break even
Price
sensitivity
LTV
Pre-sales
...
Political & legal enviroment
Political enviroment
Legal framework
Asset characteristics
Competition
Location
Design
Asset condition
Strength of sponsor and
developer
Share in
equity
Cost overrun
Reputation
Network strength
Security package
Collateral
Income control
SPV
IPRE model vs standard AHP methodology
Usually in AHP options are cardinal variables, while in IPRE they are on
ordinal scale (4 slotting grades: from 1 – strong to 4 – weak)
This has impact on the first step:
17
RATING RATING
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
SLOT1 SLOT1 SLOT2 SLOT2 SLOT3 SLOT3 SLOT4 SLOT4
IPRE model vs standard AHP methodology
Pairwise matrix for each subcriterion is not constructed (it is meaningless to
compare one slot to the other)
Alternative approach: for every subcriterion we construct vector that classifies
that subcriterion to a certain slot, e.g. one subcriterion classified to 3rd slot:
After that process is the same as in standard AHP methodology 18
RATING RATING
C1 C1 C2 C2 C3 C3
SC1 SC1 SC3 SC3 SC5 SC5 SC2 SC2 SC4 SC4 SC6 SC6
SLOT1 SLOT1 SLOT2 SLOT2 SLOT3 SLOT3 SLOT4 SLOT4
0
0
1
0
Slot 1
Slot 2
Slot 3
Slot 4
Validation
Low default portfolio – usual backtesting not feasible
Entire IPRE portfolio of the bank was rated by 3 departments:
Sales
Underwriting
Monitoring
Consistency of rating distribution among these departments indicate model
quality
Consistency was calculated using ratings matrix and slots drift, e.g:
19
Credit Risk Underwriting
Sales
1 2 3 4 Total
1 20 15 3 0 38
2 0 21 16 0 37
3 0 0 37 8 45
4 0 0 0 15 15
Total 20 36 56 23 135
Slots drift
0 69%
+1 or 1 29%
+2 or -2 2%
+3 or -3 0%
Conclusion
Strengths:
Simple
Interpretable
Usage of domain experts’ knowledge
Weaknesses:
Time consuming
Decision fatigue (drop of concentration)
Correlation between subcriteria (treshold for correlation?)
20
References
T.L. Saaty, “The Analytic Hierarchy Process: Planning, Priority Setting, Resource
Allocation”, McGraw Hill, 1980.
T.L. Saaty, “Decision making with the analytic hierarchy process“, Int. J. Services
Sciences, vol. 1, no. 1, 2008.
BIS Basel Committee on Banking Supervision, Basel II: “International Convergence
of Capital Measurement and Capital Standards: A Revised Framework” –
Comprehensive Version, 200
Directive 2006/48/EC of the European Parliment and of the Council, 2006.
Basel Committee on Banking Supervision, “ Working Paper on the Internal Ratings-
Based Approach to Specialised Lending Exposures“, 2001.
N. Saardchom, “ The validation of analytic hierarchy process (AHP) scoring model“,
International Journal of Liability and Scientific Enquiry, vol. 4, no. 2, pp. 163-179, 2012.
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Igor Kaluđer [email protected]
Ivan Augustin [email protected]
Mladen Dragičević [email protected]
Contacts