Economics Department
Centre for Computational Finance and Economic Agents
Systemic Risk From Global Financial Derivatives: A
Network Analysis of Contagion and Its Mitigation With
Super-Spreader Tax
Presentation at Monetary and Capital Markets Department ,
International Monetary Fund , Washington DC
7 Dec 2011
Sheri Markose
scher@essex.ac.uk
The software used in network modelling was developed by
Sheri Markose with Simone Giansante and Ali Rais
Shaghaghi
Roadmap:
• Overview
• New Office of Financial Research in the US Treasury to put
an end to regulators flying blind
• Financial Contagion and Systemic Risk :Statistical v.
Structural Networks Model
• Large Complex Financial Intermediaries and Global
Financial Derivatives
• Some technical details on Network Modelling
• Topological Concentration: Too Interconnected to Fail
(TITF)
• Stability of Networks and Eigenvector Centrality
• Internalizing Systemic Risk of ‘Superspreaders’ (Andrew
Haldane 2009 idea operationalized by Markose (2011))
• Empirical Calibration of Global Derivatives Model and
Financial Contagion
• Furfine Stress Test
• Superspreader Lite Escrow Fund
• Results
• Conclusions
Banking Stability Index (Segoviano, Goodhart 09/04) v
Market VIX and V-FTSE Indexes : Sadly market data based
indices spike contemporaneously with crisis ; devoid of
requisite info for Early Warning System
Fallacy of Composition In the Generation of
Systemic Risk/Negative Externalities: Holistic
Visualization Needed
Systemic risk refers to the larger threats to the financial system as a whole that
arise from domino effects of the failed entity on others.
Systemic risk from financial derivatives came to the forefront with growth in
credit derivatives to about $60 tn at its peak in 2006 and with it the excessive
liabilities on credit default swaps (CDS) of key institutions such as American
Insurance Group (AIG)
Tax payer bailouts ($14 Trillion) under the rubric of ‘too interconnected to fail’.
Risk sharing in advanced economies uses O-T-C derivatives. At the level of
the individual user these schemes appear plausible but at the macrolevel may lead to systemically unsustainable outcomes. Success of risk
sharing at a system level depends on who is providing insurance and
structural interconnections involved in the provision of guarantees.
Only 5% of world OTC derivatives is for hedging purposes
Credit Risk Transfer in Basel 2 gave capital reductions from 8% to 1.8% capital
charge if banks got CDS guarantees from ‘AAA’ providers . Most of this held
$674 Trillion Gross Notional Dec 2009


When compared to the size of world GDP at $70 tn, and
size of the global bond market (total debt outstanding) at
about $82 tn, the implication is that the size of off balance
sheet activities of financial intermediaries (FIs) has grown
to many multiples of their assets
Procyclical derivatives obligations of FIs under conditions
of market wide adverse movements on the underlying
(such as interest rates, house prices, exchange rates,
external debt of countries including sovereign debt) could
overwhelm the equity and assets of FIs.
Structure of Global Financial Derivatives
Market (2009,Q4 202 participants): Green(Interest Rate), Blue (Forex),
Maroon ( Equity); Red (CDS); Yellow (Commodity); Circle in centre Broker
Dealers in all markets
UK Fund Management 1984 and 2004 (Source Blake et.
al 2010) Fund sponsors think they are diversifying by
outsourcing to specialist fund managers:
concentration and herding at system level
Topological Concentration


2009 Fitch survey: “dependence on a limited number of
counterparties looks to be a permanent feature of the market;
this is underscored by the fact that the top 12
counterparties comprised 78% of total exposure in
terms of the number of times cited, up from the 67%
reported last year. The top five institutions that provided
volume figures accounted for 95% of total notional amount
bought and sold. This concentration increased after the
collapse of a number of financial institutions who were
important intermediaries in this market.”
http://www.scribd.com/doc/37557210/Fitch-Market-ResearchGlobal-Credit-Derivatives-Survey-09162010 .
These are Goldman Sachs, JP Morgan Chase, Barclays, Bank of
America, Deutsche Bank, Morgan Stanley, Credit Suisse, BNP
Paribas, UBS, Bank of America, Merrill Lynch, Royal Bank of
Scotland.
Notional amounts outstanding: Bns
70000
800000
60000
700000
600000
50000
500000
40000
30000
20000
Equity-linked contracts
400000
Commodity contracts
300000
Credit default swaps
200000
10000
100000
0
Gross market values (£bns)
Foreign exchange contracts
0
6000
5000
Total contracts(right axis)
Interest rate contracts(right
axis)
40000
35000
30000
4000
3000
2000
Foreign exchange contracts
Equity-linked contracts
25000
20000
Commodity contracts
15000
Credit default swaps
10000
1000
0
5000
0
Total contracts(right axis)
Interest rate contracts(right
axis)
Total Value and Market Share of Financial Derivatives for Banks
(1)The total value of financial derivatives is in billions of US dollars. (2) The
market shares are in parenthesis. (3) Banks are ranked using Gross Notional
Gross Notional
All FIs
674.369
Gross Positive Fair
Value (GPFV)
Gross Negative
Fair Value
(GNFV)
Derivatives Assets
10.465
Derivatives
Liabilities
Total Assets
0.889
37.252
Tier 1 capital
1.413
10.144
1.168
Top 16 FIs
659.263
(97.76%)
10.254
(97.98%)
9.934
(97.92%)
Top 26 FIs
673. 827
(99.92%)
10.453
(99.89%)
10.134
(99.89%)
1.068
(91.39%)
0.816
(91.78%)
27.863
(74.80%)
1.014
(71.60%)
1.15
(98.52%)
0.874
(98.33%)
32.837
(88.15%)
1.207
(85.48%)
Three major methodological issues:Why no
dogs barked ?
1. Why was the need for macroprudential framework eschewed?
Mainstream Neoclassical ‘Representative Agent’ Models;
Unfortunate Irrelevance of Most State of the Art Monetary
Economics (Buiter 09)
2.Why were there no system wide quantitative models developed for
stress tests of how the financial network would function under these
micro regulatory rules of individual bank behaviour?
Failure of macro-econometric models for policy analysis (Lucas
Critique);we have yet to replace this with multi-agent fine grained
data base driven financial network models
3. Urgent need for modelling tools to monitor liquidity gridlocks,direction
of an ongoing financial contagion, systemic risk : Multi-Agent
Financial Network Models
Answer: Lack of Complex Adaptive System framework- Red Queen
type competitive co-evolution esp between regulator and regulatee
requires constant vigilance and production of countervailing
measures(Markose 2004, 2005) Robert Axelrod on Fragility of
Communication Networks : Overlook Competitive Co-evolution
Structural vs Statistical Contagion
•
DEFINITION: Economic and financial contagion refers to the spreading
of a negative shock on the solvency conditions of an economic or
financial entity in a physical supply chain or in terms of generic
credit/debt and liquidity obligations governing interbank, payment and
settlement systems and/or claims on other financial markets
•
Structural model based on default causality of chain reactions
governed by the network connections of the financial entities
•
In contrast, models made popular by Kaminsky and Reinhart (2000)
view financial contagion as the downward co-movement of asset
prices across different markets and for different asset classes. This is
based on statistical or econometric methods which measure (amongst
other ways) the increased correlations of asset prices
Above models complimentary to the causal default models that use
financial network simulations, especially in the use of contagion
models based on CDS price co-movements (Jorge Chan-Lau et al.,
2009)
•
CDS Spreads based Statistical Models of
Contagion Only quantitative assessment of FIs’ overall derivatives
exposure and systemic risk impact : Sergoviano and Singh (IMF, 2010).
Segoviano and Singh (IMF, 2010) :To quantify counterparty risk,
estimate the probability that, given that a particular institution
(counterparty) fails to deliver, other institutions in the system would
also fail to deliver. Conditional probabilities quantifies Distress
Dependence among the FIs that have obligations in the OTC
derivative market. They use the CDS spreads on FIs to determine
conditional probability of defaults
Segoviano-Singh find that the expected cumulative derivatives
losses when cascaded in a series of insolvencies of top broker
dealers are even beyond the capabilities of the Fed Reserve to
provide backstops.
This adds urgency for the need to conduct an in-depth structural
analysis of the financial derivatives and the role of large FIs.
Key empirical variables derivatives liabilities and assets: involves
derivatives payable by each FI with legally binding bilateral
obligations netted over all OTC derivatives products and adjusted
Financial network models to date have yielded mixed results :
None about propagators of 2007 crisis (C: Core; P: Periphery PP
below mostly zero yielding very sparse matrix)
Properties of Networks
Diagonal Elements Characterize Small World Networks
Watts and Strogatz (1998), Watts (2002) See Markose et. al. (2004)
Properties Clustering
Coefficient
Average Path
Length
Degree
Distribution
High
Equal and fixed
In-degrees to each
node
Networks
Regular
High
Random
Low
Low
Scale Free/Power
Law
Low
Variable
Exponential/
Poisson
Fat Tail
Distribution
Some Network Concepts:A graphical representation of uncorrelated
random graph (left) and small world graph with hubs, Markose et. al. 2004
Work Done by Sheri Markose and Simone Giansante
for the Reserve Bank of India in mapping the financial
system shows the following networks structures (PTO)
• Top RHS Derivatives Exposures : Shows highly
tiered Craig-von Peter (2011)core-periphery structure
with large numbers of participants in the periphery
and a few in the core
• Top LHS Interbank Exposures: Shows a more
diffused core with more numbers of banks in the core
• Bottom: network for Indian RTGS (large value
payment and settlement systems) shows no marked
tiering with few financial institutions in the periphery
• Above increasing seen as stylized facts for network
structures in different financial sectors
Financial Derivatives for the top 22 banks ($ billion)
JPMORGAN
CHASE
Royal Bank
of Scotland
Bank of
America
Deutsche
Bank
Barclays
Group PLC
BNP
PARIBAS
Credit
Suisse
Morgan
Stanley
Goldman
Sachs
Citibank
UBS Bank
Global
Credit
Agricole
HSBC Group
Unicredit
Lloyds
Societe
General
ICE Trust
U.S.
Standard
Chartered
Dexia
Wachovia
bank
Bank of New
Gross
Notional
78,665
(11.66%)
76,377
(11.33%)
72,529
(10.76%)
71,040
(10.53%)
61,144
(9.07%)
59,697
(8.85%)
44,550
(6.61%)
41,506
(6.15%)
41,118
(6.10%)
36,087
(5.35%)
28,013
(4.15%)
21,698
(3.22%)
14,477
(2.15%)
4,978
(0.74%)
3,784
(0.56%)
3,601
(0.53%)
3,302
(0.49%)
2,905
(0.43%)
2,629
(0.39%)
2,263
(0.34%)
1,275
GPFV
1,550
(14.81%)
690
(6.59%)
1,494
(14.28%)
867
(8.28%)
649
(6.21%)
522
(4.99%)
735
(7.02%)
928
(8.86%)
654
(6.25%)
706
(6.74%)
436
(4.16%)
351
(3.36%)
247
(2.36%)
110
(1.05%)
60
(0.58%)
254
(2.43%)
4
(0.04%)
38
(0.36%)
44
(0.42%)
66
(0.63%)
16
GNFV
1,517
(14.95%)
663
(6.53%)
1,462
(14.41%)
834
(8.22%)
628
(6.19%)
493
(4.86%)
734
(7.23%)
890
(8.77%)
591
(5.83%)
690
(6.80%)
424
(4.18%)
348
(3.43%)
248
(2.44%)
112
(1.10%)
50
(0.49%)
251
(2.48%)
4
(0.04%)
37
(0.36%)
46
(0.45%)
66
(0.65%)
17
Derivatives
Assets
95
(8.16%)
106
(9.09%)
81
(6.91%)
100
(8.53%)
65
(5.57%)
60
(5.17%)
59
(5.07%)
49
(4.20%)
45
(3.88%)
87
(7.46%)
74
(6.31%)
70
(5.99%)
58
(4.95%)
89
(7.58%)
29
(2.51%)
0
(0.00%)
0
(0.00%)
8
(0.66%)
12
(1.00%)
29
(2.46%)
8
Derivative
Liabilities
81
(9.15%)
81
(9.08%)
44
(4.91%)
67
(7.58%)
49
(5.49%)
31
(3.54%)
60
(6.79%)
38
(4.30%)
24
(2.71%)
53
(5.95%)
66
(7.45%)
57
(6.42%)
58
(6.53%)
90
(10.11%)
16
(1.77%)
0
(0.00%)
0
(0.00%)
6
(0.68%)
14
(1.52%)
9
(1.04%)
9
Total
Assets
2,692
(7.23%)
2,379
(6.39%)
2,855
(7.66%)
2,156
(5.79%)
2,155
(5.78%)
2,956
(7.93%)
1,066
(2.86%)
773
(2.08%)
182
(0.49%)
1,764
(4.74%)
1,385
(3.72%)
2,237
(6.01%)
1,175
(3.15%)
1,334
(3.58%)
1,605
(4.31%)
1,150
(3.09%)
6
(0.02%)
437
(1.17%)
830
(2.23%)
997
(2.68%)
250
Tier 1
Capital
96
(6.82%)
98
(6.96%)
112
(7.92%)
49
(3.50%)
78
(5.49%)
90
(6.40%)
39
(2.80%)
47
(3.30%)
17
(1.21%)
97
(6.85%)
42
(3.00%)
45
(3.15%)
35
(2.51%)
56
(3.97%)
74
(5.26%)
35
(2.46%)
0.45,624
(1.38%)
25
(1.74%)
25
(1.79%)
40
(2.82%)
10
Financial Networks for the Derivatives Obligations: High Clustering
from broker dealer behaviour and Barabasi et. al. Preferential
attachment model very sparse matrix
• Our algorithm assigns out degrees for a bank in terms of
its respective market shares (siB/G) for Derivatives
purchases(B) and sales (G), resp. Key is M Matrix of
Netted elements of Gross Flow X Matrix below
Data
Federal Deposit Insurance Corporation (FDIC) Call Report
2009 4th quarter for smaller US banks treated as national associations
Larger global banks data obtained from individual financial reports
204 x 204 matrix : 202 European and US banks & financial institutions +
aggregation of all Insurance companies + exposure to all banks outside Europe
and USA considered together
Rows are gross negative fair value, i.e., market valued obligation from row
bank to column bank
JPMORGAN
0
BoA
222.913336
Morgan
Stanley
138.374
221.42
0
124.155
116.339
104.958
100.795
Morgan Stanley
126.661
122.075497
0
70.7962
60.0402
57.6591
Deutsche Bank
118.784
114.4837229
71.0663
0
56.3063
54.0734
Credit Suisse
105.095
101.290621
62.8766
58.7422
0
47.842
CITIBANK
95.8675
92.39670082
57.3556
53.5843
45.4433
0
JPMORGAN
BoA
Deutsche
Bank
129.276
Credit Suisse
109.635
CITIBANK
105.287
Units: Billions of dollars
Constructing the network of bilateral exposures
X=
0
221.42
126.66
118.78
105.10
95.87
…
222.91 138.37 129.28 109.64 105.29 …
0 124.15 116.34 104.96 100.80 …
122.08
0 70.80 60.04 57.66 …
114.48 71.07
0 56.31 54.07 …
101.29 62.88 58.74
0 47.84 …
92.40 57.36 53.58 45.44
0…
…
…
…
…
……
M = X – XT : antisymmetric matrix of derivatives payables
mij > 0 is net payables by node i from node j
mji = – mij is corresponding amount by j to i
Considering only matrix of +ve values, i.e., m+ij = mij if mij >0, mij= 0 otherwise
we obtain the weighted adjacency matrix for the directed network
M+ =
0 1.49 11.71 10.49
0
0 2.08 1.86
0
0
0
0
0
0 0.27
0
0
0 2.84 2.44
0
0
0
0
…
…
…
…
4.54
3.67
0
0
0
0
…
9.42 …
8.40 …
0.30 …
0.49 …
2.40 …
0…
……
links point from the
derivatives net seller
to the net buyer (the
direction of contagion)
Contagion and Stability of Matrix Θ’ :
Impact of i on j relative to j’s capital


0



0


.


(
x

x
)
 i1 1i

C1t

.


(
x

x
)
 N 1 1N

C1t
( x12  x21 ) 
C2 t
.
( x13  x31 ) 
C3t
( x23  x32 ) 
C3t
0
.
...
0
...
.
...
0
.
...
...
( xNj  x jN ) 
0
.0.
....
....
....
....
....
C jt
...

0



( x3 N  xN 3 ) 

C Nt

.
 (2)
( xiN  xNi ) 

C Nt

.


0

Global Derivatives Market (Θ matrix) : JP and BoA
central Tier; 22 other banks in Tier 2 all banks in the
top tiers will fail if any other fails of this group
We will use the rich club coefficient, (k) to
identify highly connected nodes who form
the club which is characterized by a fully
connected network. The latter yields a
coefficient of 1 and k# will denote the critical
number of out-degrees the nodes need to
have to be part of the largest sized rich club
with (k) =1.
Eigenvector Centrality
A variant is used in the Page Ranking algorithm used by Google
Centrality: a measure of the relative importance of a node
within a network
Eigenvector centrality
Based on the idea that the centrality vi of a node should be proportional to
the sum of the centralities of the neighbors
 is a constant
The vector v, containing centrality values of all nodes is obtained by solving
the eigenvalue equation Θ v = λmax v
and selecting the eigenvector corresponding to the largest eigenvalue
Positive values for the centralities are guaranteed by Perron-Frobenius thm:
The eigenvector of the largest eigenvalue of a non-negative matrix Θ’ has
only positive components.
U0 with elements (u1t , u2t, ..... unt) = (1,0,......0) to
indicate the trigger bank that fails at initial date,
t=0, is bank 1 and the non-failed banks assume 0’s
Dynamics of bank failures given by:
Ut +1
= ´Ut - I
(10)
There are 4 ways in which stability of the
financial network can be achieved
(i)Constrain the bilateral exposure of financial
intermediaries.This will only be successful relative to λmax
(ii) Increase the threshold rho in (11),
(iii) Change the topology of the network
(iv)Levy a capital surcharge commensurate to the
eigenvector centrality of a financial institution in (11).
(i) & (ii) do not price in negative externalities and systemic
risk of failure of highly network central nodes. Network
topologies emerge endogenously and are hard to manipulate
exogenously.
Network Statistics –Scaling exponent (alpha)
for outdegrees and for flows/exposures : those
with higher connectivity have even higher
liabilities (V1 204 nodes; V2 202 nodes)
Connectivity
Outdegree (V1)
Clustering
0.018
0.48
Flows (V1)
Outdegree(V2)
Flows (V2)
0.013
0.45
Tail
MaxExponent Xmin Likelyhood
2.1
1 -225.806
2.49
7.95 -167.081
2.15
1 -209.727
3.38
7.95 -97.2634
Rich Club Statistics
Out Degree
(k)
k>0
k>1
k>2
k>3
k>4
k>6
k>7
k>8
k>9
k>10
k>12
k>13
k>16
Rich Club Coefficient
0.03
0.22
0.38
0.64
0.67
0.69
0.71
0.91
0.95
1
1
1
1
Number of
Nodes(N(k))
150
42
30
21
20
19
18
13
11
9
6
4
3
Too Interconnected To Fail :
Stress Test
• Objective: Build Network based on Θ’ and Conduct Stress Tests
There is very high correlation between the dominance of market
share in CDS and CDS network connectivity
• Stress Tests: Follow Furfine (2003) Algorithm
• The loss of derivatives cover/receivables due to the failed bank as
counterparty suspending its guarantees will have a contagion like
first and multiple order effects. Full bilateral tear up assumed; No
possibility for Novation
• There is a power iteration Θ’ q where q is the qth power of the
netted matrix. At each q, weighted paths of length q
between each i and j nodes is obtained
•
We use 6% reduction of core capital to signal bank failure
Table 5 2009 Q4 Eigenvector Centrality (EVC) (for Top 20 FIs ranked by weighted EVC)
Trigger Bank
and
membership of
Rich Club*
Tier 1
Capital
Links(In&Out)
EVC
(unwted)
EVC
(wted)
$ loss at
q=1;6%
threshold
(0%)
Goldman Sachs
17.15
33 (0.078)
0.26
0.39
3.97(20.20)
Deutsche Bank
JPMorgan
Credit Suisse
Morgan Stanley
HSBC Group
Societe
Generale(0.38)
Barclays
Bank of
America
Standard
Chartered
(0.22)
49.42
96.37
39.49
46.67
23 (0.054)
71 (0.15)
16 (0.038)
33 (0.08)
0.25
0.31
0.20
0.26
0.32
0.31
0.30
0.30
13.93(27.01)
32.38(69.78)
11.28(33.01)
5.72(16.77)
35.48
10 (0.024)
0.15
0.30
39.73(66.17)
34.69
10 (0.023)
0.15
0.24
16.10(31.40)
77.56
21 (0.049)
0.26
0.23
20.42(40.96)
111.92
54 (0.13)
0.29
0.21
4
4
4
6
4
10
4
4
6
3
8
8
6
2
24.58
9 (0.021)
0.14
0.19
3.93(8.24)
0.26
0.18
8.89(24.34)
Wachovia
39.79
21 (0.049)
0.16
0.17
9.82(25.12)
Uni Credit
12
12.08(43.19)
30 (0.07)
Lloyds
5
7
96.83
Credit Agricole
7
Conditional
failure of
FI when
others fail
3
Citibank
BNP Paribas
Contagion
of Trigger:
FIs Failed
q=1
90.37
44.53
74.27
56.07
21 (0.049)
10 (0.024)
10 (0.024)
5(0.012)
10 (0.024)
0.24
0.15
0.15
0.07
0.15
0.15
0.14
0.14
0.13
0.13
7.16 (28.07)
9.68 (42.44)
9.29(19.28)
15.88(25.97)
UBS
New York
Mellon
42.32
5(27.31)
10.15
18 (0.042)
0.15
0.11
0(9.26)
RBS
98.28
25 (0.059)
0.26
0.07
0.37 (5.70)
1
5
3
9
8
3
3
4
5
3
9
5
3
2
3
0
0
4
2
Dexia(0.22)
25.24
6 (0.013)
0.06
0.06
5.23(10.75)
NB * Purple stands for the rich club coefficient (k>11)=1 ; Brown (k>9)= 0.95; Green (k>8)= 0.91
1
1
Contagion from JP Morgan (LHS; 12
direct counterparties) BoA (RHS; 7 direct
counterparties )
Contagion from
Deutsche Bank (LHS; 4 direct c-parties
demised) Standard Charter (RHS; 1 direct cparty demises)
Contagion when JP Morgan Demises in Clustered CDS Network 2008
Q4 ( Left 4 banks fail in first step and crisis contained) v
In Random Graph (Right 22 banks fail !! Over many steps)
Innoculate some key players v Innoculate all ( Data Q4 08)
Socialization of Losses
Sergoviano and Singh (IMF 2008) Based on March 2008
data, in the case of a single institution failure, the total
loss could be as high as $300–$400 billion depending
on the FI; but when cascade effects are taken into
account, the total loss could rise to over $1,500 billion.
Our 2009 Q4 results show direct domino losses
$ 350.6bn constituting 25% loss of Tier 1 capital of
banks ; this does not include non-banks or nonUS/European banks; on including latter capital losses
closer to $750 bn
A super-spreader lite tax fund can be designed of only
$66 bn (see Table 7 to follow) to cover 1st tier of the rich
club
How to stabilize ?: Superspreader tax
quantified : tax using Eigenvector centrality
of each bank vi or vi^2 to reduce max
eigenvalue of matrix from 1.48
Superspreader tax rate
Table 7 Super-Spreader Tax Raised From Top 20 LCFIs (All
columns other than EVC $bns) PTO
Note EVC is Eigenvector Centrality ; Tax % = EVC x alpha;
Tax$s= Tax Rate x Tier 1 Capital
• Super-spreader fund works like an escrow
account; amounts escrowed as in a CCP or by
regulator to be disbursed when default occurs
• Super Spreader Fund lite : Secure funds to
cover max losses of 1st tier (q=1) from any
trigger bank failure
• Full stabilization for λmax < 1, costly implies tax
rates of 77% of Tier 1 capital of Goldman Sachs
etc
Alpha
0.2
Bank Name
T ier 1 Capital
0.3
0.5
EVC T ax% T ax $s T ax % T ax $s T ax%
1.00
1.5
T ax
$s
T ax% T ax $s T ax%
6.64
T ax
$s
T ax%
T ax
9.96
0.77
13.28
Goldman Sachs
17.15
0.39
0.08
1.33
0.12
1.99
0.19
3.32
0.39
Deutsche Bank
49.42
0.32
0.06
3.20
0.10
4.80
0.16
7.99
0.32 15.99
0.49 23.98
0.65
31.98
JPMorgan
96.37
0.31
0.06
6.04
0.09
9.06
0.16 15.09
0.31 30.19
0.47 45.28
0.63
60.37
Credit Suisse
39.49
0.30
0.06
2.39
0.09
3.58
0.15
5.97
0.30 11.94
0.45 17.91
0.60
23.87
Morgan Stanley
46.67
0.30
0.06
2.80
0.09
4.20
0.15
7.00
0.30 14.00
0.45 21.00
0.60
28.00
HSBC Group
35.48
0.30
0.06
2.13
0.09
3.19
0.15
5.32
0.30 10.63
0.45 15.95
0.60
21.26
Societe Generale
34.69
0.24
0.05
1.64
0.07
2.46
0.12
4.10
0.24
8.20
0.35 12.30
0.47
16.41
Barclays
77.56
0.23
0.05
3.64
0.07
5.46
0.12
9.10
0.23 18.20
0.35 27.29
0.47
36.39
Bank of America
111.92
0.21
0.04
4.61
0.06
6.92
0.10 11.53
0.21 23.05
0.31 34.58
0.41
46.11
Standard Chartered
24.58
0.19
0.04
0.94
0.06
1.40
0.10
2.34
0.19
0.29
7.02
0.38
9.36
Citibank
96.83
0.18
0.04
3.52
0.05
5.29
0.09
8.81
0.18 17.62
0.27 26.43
0.36
35.25
Wachovia
39.79
0.17
0.03
1.38
0.05
2.08
0.09
3.46
0.17
6.92
0.26 10.38
0.35
13.84
BNP Paribas
90.37
0.15
0.03
2.70
0.04
4.06
0.07
6.76
0.15 13.52
0.22 20.28
0.30
27.03
Credit Agricole
44.53
0.14
0.03
1.27
0.04
1.90
0.07
3.17
0.14
0.21
9.50
0.28
12.67
Lloyds
74.27
0.14
0.03
2.09
0.04
3.14
0.07
5.23
0.14 10.45
0.21 15.68
0.28
20.90
Uni Credit
56.07
0.13
0.03
1.45
0.04
2.18
0.06
3.63
0.13
7.26
0.19 10.89
0.26
14.52
UBS
42.32
0.13
0.03
1.09
0.04
1.63
0.06
2.72
0.13
5.45
0.19
8.17
0.26
10.90
New York Mellon
10.15
0.11
0.02
0.22
0.03
0.33
0.05
0.55
0.11
1.11
0.16
1.66
0.22
2.21
RBS
98.28
0.07
0.01
1.35
0.02
2.03
0.03
3.39
0.07
6.77
0.10 10.16
0.14
13.54
Dexia
25.24
0.06
0.01
0.31
0.02
0.46
0.03
0.76
0.06
1.53
0.09
0.12
3.06
4.68
6.34
0.58
2
2.29
Conclusion :Systems are unstable and superspreader taxes aim to mitigate instability
• Too interconnected to fail addressed only if systemic risk from
individual banks can be rectified with a price or tax reflecting the
negative externalities of their connectivity
• Lessons to be learnt : Disease Transmission in scale free networks
(May and Lloyd (1998), Barthelemy et. al : With higher probabilities
that a node is connected to highly connected nodes means disease
spread follows a hierarchical order.
• Highly connected nodes become infected first and epidemic dying
out fast and often contained in first two tiers
• Cold comfort for financial networks as failure of superspreaders
destroys bulk of Tier 1 capital and history as we know it is over !
• However, tiered systems easier to target and manage than
uncorrelated random graphs
• Innoculate a few rather than whole population; Strengthen hub;
Reduce variance of node strength in dominant eigenvalue formula
• Changes in eigenvector centrality of FIs can give early warning of
instability causing banks
Ongoing tests and Concluding Remarks
• Derivatives do not complete markets; excessive
use causes tail risk; extant size a threat
• Super spreader tax and fund recommended over
ad hoc breakup of banks
• Can eigenvector centrality based on adjacency
matrix ie. unweighted eigenvector centrality be a
sufficient proxy ?; less information is needed
• Capital for CCPs to secure system stability can
use same calculations based on eigenvector
centrality
• Further stress tests for robustness of ICE to see
if .0013% capital is sufficient
• Slides overleaf underscore my strong belief that
financial networks should be calibrated on the
basis of empirical concentration and clustering
Other Issues :Do Real World Financial
Networks Satisfy Nash Equilibrium ?
Babus (2009) states that in “an equilibrium network the
degree of systemic risk, defined as the probability that
a contagion occurs conditional on one bank failing, is
significantly reduced”. The premise of too
interconnected to fail is that the failure of a big bank
will increase the failure of another big bank, which we
find to be the empirical characteristic of the network
topology of the derivatives market involving LCFIs,
indicates that the drivers of network formation in the
real world are different from those assumed in
economic equilibrium models.
Ballester et al (2006 Econometrica) Quadratic utility
and Nash equilibrium of economic activity:
(wi/Aggregate wi ) = (Ratio of Bonacich centrality of i to
sum of BC ) No evidence of equality
Ratios for top 20 banks by the Weighted Katzbonacich measure
HSBC Group
JPMORGAN
Credit Agricole
SOCIETE
GENERAL
Uni_Credit
BANK_OF_AMER
ICA
Barclays_Group_
PLC
Credit_Suisse
WACHOVIA_BAN
K
Ratio of banks KRatio of banks K- Market share of
B/Total K.B
B / Total K.B.
each bank for
(unweighted)
(weighted)
derivatives liabilities
0.00886
0.012587
0.0968908
0.018661
0.011858
0.1034948
0.010081
0.010829
0.077865
0.006924
0.006087
0.010788
0.010333
0.0678722
0.0727396
0.017091
0.009603
0.0683279
0.010365
0.009543
0.009392
0.009269
0.0530993
0.0564319
0.008252
0.008922
0.0481663
University of Essex, Econ Dept WP Feb 2010 No. 683
Financial Contagion and Systemic Risk in Network
Model of CDS and Other Credit Enhancement
Obligations of US Banks (pdf version) [Abstract]
Simulator link CDS Network Simulator
http://www.acefinmod.com/CDS1.html