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Sovereign, Bank, and
Insurance Credit
Spreads: Connectedness
and System Networks
SYstemic Risk TOmography:
Signals, Measurements, Transmission Channels,
and Policy Interventions
Monica Billio (Ca’ Foscari University of Venice), Mila Getmansky
(University of Massachusetts), Dale Gray (IMF), Andrew W. Lo (MIT &
AlphaSimplex Group, Cambridge), Robert C. Merton (MIT) and Loriana
Pelizzon (Ca’ Foscari University of Venice)
Brescia, 25 June 2013
2
Objectives
• The risks of the banking and insurance systems have 
become increasingly interconnected with sovereign 
risk
• Highlight interconnections: 
• Among countries and financial institutions 
• Consider both explicit and implicit connections
• Quantify the effects of:
• Asset‐liability mismatches within and across 
countries and financial institutions
3
Methodology
• We propose to measure and analyze 
interactions between financial 
institutions, sovereigns using:
– Contingent claims analysis (CCA) 
– Network approach
4
Background
• Existing methods of measuring financial stability 
have been heavily criticized by Cihak (2007) and 
Segoviano and Goodhart (2009):
• A good measure of systemic stability has to 
incorporate two fundamental components: 
– The probability of individual financial 
institution or country defaults
– The probability and speed of possible shocks 
spreading throughout the industry and 
countries
5
Background
• Most policy efforts have not focused in a 
comprehensive way on: 
– Assessing network externalities 
– Interconnectedness between financial institutions, 
financial markets, and sovereign countries 
– Effect of network and interconnectedness on 
systemic risk
Background: Feedback Loops of Risk 
from Explicit and Implicit Guarantees
Source: IMF GFSR 2010, October Dale Gray
6
7
Background
• The size, interconnectedness, and complexity of 
individual financial institutions and their inter‐
relationships with sovereign risk create 
vulnerabilities to systemic risk
• We propose Expected Loss Ratios (based on CCA) 
and network measures to analyze financial 
system interactions and systemic risk
Core Concept of CCA: 
Merton Model 
• Expected Loss Ratio = Cost of Guar/RF Debt
= PUT/B exp[‐rT]
= ELR 
• Fair Value CDS Spread = ‐log (1 – ELR)/ T
8
9
Moody’s KMV CreditEdge for Banks and 
Insurance Companies
• MKMV uses equity and equity volatility and default barrier (from 
accounting information) to get  “distance‐to‐ distress” which  it maps 
to a default probability (EDF) using a pool of 30 years of default 
information
• It then converts the EDF to a risk neutral default probability (using the 
market price of risk), then using the sector loss given default (LGD) it 
calculates the Expected Loss Ratio (EL) for banks and Insurances:
EL Ratio = RNDP*LGDSector
• It calculates the Fair Value CDS Spread
Fair Value CDS Spread = ‐1/T ln (1 – EL Ratio) 
Why EL Values?
• EL Values are used because they do not have the 
distortions which affect observed CDS Spreads
• For banks and some other financial institutions:
• The fair‐value CDS spreads (implied credit spreads 
derived from CCA models, i.e. derived from equity 
information) are frequently > than the observed 
market CDS
• This is due to the depressing effect of implicit and 
explicit government guarantees
Why EL Values?
• In other cases, e.g. in the Euro area periphery countries, 
bank and insurance company CDS appear to be affected 
by spillover from high sovereign spreads (observed CDS 
> FVCDS). 
• For these reasons we use the  EL associated with the 
FVCDS spreads for banks and insurance companies 
which do not contain the distortions of sovereign 
guarantees or sovereign credit risk spillovers
Sovereign Expected Loss Ratio
• CCA has been applied to sovereigns, both emerging market and 
developed sovereigns
• Sovereign CDS spreads can be modeled from sovereign CCA models 
where the spread is associated with the expected loss value and 
sovereign default barrier 
• For this study the formula for estimating sovereign EL is 
simply derived from sovereign CDS
EL Ratio Sovereign  = 1‐exp(‐(Sovereign CDS/10000)*T)
• EL ratios for both banks and sovereigns have a horizon of 5 
years (5‐year CDS most liquid)
Linear Granger Causality Tests
ELRk (t) = ak + bk ELRk(t‐1) + bjk ELRj(t‐1) + Ɛt
ELRj(t) = aj +  bj ELRj(t‐1) + bkj ELRk(t‐1) + ζt
• If bjk is significantly > 0, then j influences k
• If bkj is significantly > 0, then k influences j
• If both are significantly > 0, then there is 
feedback, mutual influence, between j and 
k.
13
Data
• Sample: Jan 01‐Mar12
• Monthly frequency
• Entities:
– 17 Sovereigns (10 EMU, 4 EU, CH, US, JA)
– 63 Banks (34EMU, 11EU, 2CH, 12US, 4JA)
– 39 Insurance Companies (9EMU, 6EU, 16US, 
2CH, 5CA)
• CCA ‐ Moody’s KMV CreditEdge:
– Expected Loss (EL)
15
Mar 12
Blue Insurance
Black Sovereign
Red Bank
Blue Insurance
Black Sovereign
Red Bank
16
Mar 12
Blue Insurance
Black Sovereign
Red Bank
Blue Insurance
Black Sovereign
Red Bank
Network Measures
• Degrees
• Connectivity
• Centrality
•Indegree (IN): number of incoming connections
•Outdegree (FROM): number of outgoing
connections
•Totdegree: Indegree + Outdegree
•Number of node connected: Number
of nodes reachable following the
directed path
•Average Shortest Path: The average
number of steps required to reach the
connected nodes
•Eigenvector Centrality (EC): The more the
node is connected to central nodes (nodes
with high EC) the more is central (higher
EC)
18
Network Measures: 
FROM and TO Sovereign
17 X 102= 1734 potential connections FROM (idem for TO)
19
From GIIPS minus TO GIIPS
20
June 07
Blue Insurance
Black Sovereign
Red Bank
21
March 08
Blue Insurance
Black Sovereign
Red Bank
22
August 08
Greece
Blue Insurance
Black Sovereign
Red Bank
23
Spain
Blue Insurance
Black Sovereign
Red Bank
December 11
March 12US
Blue Insurance
Black Sovereign
Red Bank
IT
25
March 12
Blue Insurance
Black Sovereign
Red Bank
Early Warning Signals
0
2000
4000
6000
8000
10000
12000
14000
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
9000000
10000000
Jan01_Dec03
Apr01_Mar04
Jul01_Jun04
Oct01_Sep04
Jan02_Dec04
Apr02_Mar05
Jul02_Jun05
Oct02_Sep05
Jan03_Dec05
Apr03_Mar06
Jul03_Jun06
Oct03_Sep06
Jan04_Dec06
Apr04_Mar07
Jul04_Jun07
Oct04_Sep07
Jan05_Dec07
Apr05_Mar08
Jul05_Jun08
Oct05_Sep08
Jan06_Dec08
Apr06_Mar09
Jul06_Jun09
Oct06_Sep09
Jan07_Dec09
Apr07_Mar10
Jul07_Jun10
Oct07_Sep10
Jan08_Dec10
Apr08_Mar11
Jul08_Jun11
Oct08_Sep11
Jan09_Dec11
Apr09_Mar12
EL # of lines
forecast
forecast
26
t=March 2008 t+1=March 2009; t = Jul 2011; t+1= Feb 2012
Cumulated Exp. Loss   ≡   Expected Loss of institution i + Expected losses of 
institutions caused by i
Early Warning Signals
Cumulative losses
March 09 February 12
Coeff t‐stat R‐square Coeff t‐stat R‐square
# of in line
# of out lines 0.40 2.92 0.23 2.2
# of lines 0.87 3.5
Closeness Centrality ‐0.63 ‐2.51 ‐0.15 ‐7.0
Eigenvector 
Centrality ‐0.15 ‐4.4
0.17 0.42
27
CDS data
28
29
Comparison CDS‐KMV
30
Comparison CDS‐KMV
31
CDS: Dec 11
Spain
Blue Insurance
Black Sovereign
Red Bank
32
Spain
Dec 11 : EL‐KMV
Blue Insurance
Black Sovereign
Red Bank
33
Blue Insurance
Black Sovereign
Red Bank
CDS:Mar 12
IT
Mar 12:EL‐KMV
US
Blue Insurance
Black Sovereign
Red Bank
IT
35
Conclusion
• The system of banks, insurance companies, 
and countries in our sample is highly 
dynamically connected
• Insurance companies are becoming highly 
connected…
• We show how one country is spreading risk to 
another sovereign
• Network measures allow for early warnings 
and assessment of the system complexity
36
Thank You!
37
Assets  =         Equity      +        Risky Debt 
=         Equity      +        Default‐Free Debt – Expected Loss  Value
Assets
Equity
or Jr
Claims
Risky
Debt
• Value of liabilities    
derived from value of 
assets.
• Liabilities have 
different seniority.
• Randomness in 
asset value. 
Core Concept of CCA: 
Merton Model 
This project is funded by
the European Union under the
7th Framework Programme (FP7-SSH/2007-2013)
Grant Agreement n°320270
!
!
!
!
!
!
!
www.syrtoproject.eu
This document reflects only the author’s views. The European Union is not liable for any use that may be made of the information contained therein.

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