This document discusses the implementation of groups of connected clients (GCC) at Íslandsbanki. It defines GCC as closely linked clients that should be treated as a single risk exposure. It describes how Íslandsbanki identifies GCC by building a graph structure to link clients based on control and economic dependency. It explains how the bank generates "super groups" by sorting clients and covering descendants. The document also discusses how accounting for GCC affects capital requirements calculations under Basel 2.

1. Groups of connected clients
Implementation at Íslandsbanki
Florian Zink

2. Overview
Groups of connected clients:
• What are they?
• Why do we need them?
• How to define them?
• Implementation at Íslandsbanki
• Effect on capital requirement

3. What are they ?
Group of connected clients =
Closely linked clients that
should be treated as single
risk.
CRD
Art. 79: Categorization of
retail exposures
Art. 108: Large exposures

4. Why do we need them?
Pillar I: Asymptotic single risk factor model
z: global state of economy
G
M
E O
F N
C
I
H J D
K B
L
A P(A) = P(A|z)p(z)
P
Conditional independence: Obligors default independently given z

5. Pillar II: full diversification  granular portfolio,
other sources of correlation: sector, geography and ...
z: global state of economy
g: geography s: sector
G
M
F E N O
C
I
D
H B J
A L
P(A) = P(A|z,s)p(z,s) K
P
Conditional independence: Obligors default independently given g, z, s

6. ... idiosyncratic correlation Removal of conditional independence assumption
 Groups of connected clients
z: global state of economy
g: geography s: sector
G
M N
F E O
C
I
D
H B J
A L
K
P
Large exposures: Treat groups of connected clients as single exposure.
“Think in terms of baskets, not eggs.” (LE limits in addition to Pillar 2)

7. How to define them – whom to link ?
Two types of connections (2006/48/EC Art. 4):
(a) Control
(b) Economic dependency (revised 2009/111/EC)
Vague definitions, need interpretation
CEBS (Dec 2009): Guidelines on the implementation
of the revised large exposures regime

8. Connection due to control:
CRD, Art. 4 (45)
‘group of connected clients’ means:
(a) two or more natural or legal persons, who,
unless it is shown otherwise, constitute a
single risk because one of them, directly or
indirectly, has control over the other or others;

9. Examples of control
• direct or indirect ownership of 50% of capital
or voting power
• power to appoint majority of governing body
that exercises control (management, board of
directors)
• power to cast majority of votes
• power to coordinate management (same
persons in management of firms)

10. Groups can overlap:
GCC 1 : CL1 + Comp1 Exposure: 110
GCC2 : CL2 + Comp1 Exposure: 130

11. Exemption: Central Govmnt with risk weight 0

12. Connection due to economic dependency:
CRD Art 4 (45)
(b) two or more natural or legal persons *…+ who
are to be regarded as constituting a single risk
because they are so interconnected that, if one of
them were to experience financial problems, in
particular funding or repayment difficulties, the
other or all of the others would be likely to
encounter funding or repayment difficulties

13. Examples Economic dependency
• guarantees threatening solvency
• property owner and hard to replaceable
tenant
• dependency on single producer/vendor
• debtor and spouse (if liable)
• dependency on same main source of funding
(not replaceable; being clients of same bank
no reason to connect)

14. CEBS: No requirement to link control and economic dependency
Merge GCC.1 and GCC.2 only if economic dependency affects whole group

15. Implementation at Íslandsbanki
Credit control keeps database of (mother kt, daughter kt, link type)
no weights yet

16. Mother Daughter Link
A B ->
B C <->
B D ->
D E ->
Generate graph structure:
• nodes (clients)
• edges (connections)

17. Mother Daughter Link
A B ->
B C <->
A
B D ->
D E ->
B
Generate graph structure: C D
• nodes (clients)
• edges (connections)
E

18. Mother Daughter Link
A B ->
B C <->
A
B D ->
D E ->
B
For every node,
get all nodes that are affected
by financial problems of that node C D
(get all descendants using DFS)
E

19. Mother Daughter Link
A B ->
B C <->
A GCC.A
B D ->
D E ->
GCC.B
GCC.C B
For every node,
get all nodes that are affected
by financial problems of that node C D
(get all descendants using DFS)
GCC.D
E

20. Super groups: (remove groups fully contained in others)
• sort nodes by (#descendants, #children, kennitala)
A GCC.A
A 4 1
B 3 2 GCC.B
C 3 1 GCC.C B
D 1 1
E 0 0
C D
GCC.D
• set all nodes as uncovered
• iterate over nodes not yet covered: E
• assign highest scoring node as head of
new group
• set node and all descendants as covered

21. Super groups: (remove groups fully contained in others)
• sort nodes by (#descendants, #children, SSN)
A GCC.A
A 4 1
B 3 2
C 3 1 B
D 1 1
E 0 0
C D
• set all nodes as uncovered
• iterate over nodes not yet covered: E
• assign highest scoring node as head of
new group
• set node and all descendants as covered

22. Example:
[REMOVED]

23. Effect on capital requirements
• ÍSB Corporate portfolio
• MC simulation of loss distribution using
importance sampling
• compare with / without GCC to Basel 2

24. Problem: Which PD to use ?
z P(A|z) = P(A|~B,z) P(~B|z) + P(A|B,z) P(B|z)
Assume rating model provides P(A|z)
B C
through qualitative factors
A
Expected loss EL(A+B) = EL(A) + EL(B) = PD(A) L(A) + PD(B) L(B)
=> use loss-weighted PD