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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

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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)

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AHP METHODOLOGY



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



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:

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GOAL GOAL

C1 C1 C2 C2 C3 C3



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:

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GOAL GOAL

C1 C1 C2 C2 C3 C3



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:

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GOAL GOAL

C1 C1 C2 C2 C3 C3



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:

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GOAL GOAL

C1 C1 C2 C2 C3 C3



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:

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GOAL GOAL

C1 C1 C2 C2 C3 C3



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



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

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Model overview

Example of rating criteria for one of the submodels:

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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:

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RATING RATING

C1 C1 C2 C2 C3 C3


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


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:

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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?)

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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]

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specialized lending rating model using ahp · specialized lending rating model using ahp credit...

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