1. OECD – ECLAC WORKSHOP
New tools and methods for policy making
19 May 2014
Session 1:
Multi-Agent Financial Network Models
And Global Macro-net Models:
New Tools for Macro-Prudential Policy
Sheri MARKOSE (scher@essex.ac.uk)
Economics Dept. University of Essex,
The software used in network modelling was developed by Sheri Markose with
Simone Giansante and Ali Rais Shaghaghi

2. Roadmap 1 : Why MAFNs/Macro-Nets for Macro-
prudential policy ?
• Two methodological problems of financial contagion and systemic
risk : (i)Paradox of Volatility and the pitfalls of market price data
based systemic risk measures hence structural bilateral data based
networks modeling needed (ii) Non- trivial Negative Externalities
problem → the need for holistic visualization
• Some Applications: Systemic Risk From Global Financial
Derivatives Modelled Using Network Analysis of Contagion and
Its Mitigation With Super-Spreader Tax
• Global Macro-nets integrated with Real Side Sectoral Flow of
Funds to assess extent of economic imbalance from
financialization and also from global flows
• Some insights from Indian Financial System and Bilateral Data
based Network Modeling: Pioneering first full bilateral digital
map of financial system (Brazil and Mexico also mandating
bilateral data)

3. Macro-prudential: Systemic Risk
Management With Networks
• Holistic Visualization to overcome fallacy of composition type errors
• ICT data base driven multi-agent financial networks: glorified data
visualizations → Andrew Haldane/ Mark Buchanan Star Trek Vision
• Causal Connections v Statistical Analysis
• Minimum three elements are needed bilateral financial data
:Contracts, Counterparties, Maturity Buckets
• Integration and automation of financial data bases in a MAFN
framework aims to transform the data from a document or record
view of the world to an object-centric view (see Balakrishnan et. al.
2010), where multiple facts about the same real-world financial
entity are accessed to give a composite visualization of their
interactions with other such entities in a scalable way.

4. Roadmap 2: Systemic Risk Analytics
• Stability of Networks and Eigen-Pair Analysis:
Markose et. al. (2012)
• 3 main questions of macro-prudential regulation :
(i)Is financial system more or less stable?
(ii)Who contributes to Systemic Risk ?
(iii)How to internalize costs of systemic risk of
‘super-spreaders’ using Pigou tax based on
eigenvector centrality: Management of moral
hazard, Bail in vs Bail out : How to Stabilize system
using EIG Algorithm ?
• Generalization to multi-layer networks
● Conclusions

5. Mark ( (i )Market Data based Statistical Models of Systemic
Risk : A Case of Steadfast Refusal to Face Facts ( á la
Goodhart, 2009) ? Absence of Early Warning Signals
Major drawback of market price based systemic risk measures: they
suffer from paradox of volatility(Borio and Drehman ,2009) or paradox
of financial stability issues first addressed by Hyman Minsky (1982).
Market based statistical proxies for systemic risk (eg Segoviano and
Goodhart (2009) banking stability index, Contingent Claim Analysis
Distance to Distress Index of Castern and Kavounis (2011)) at best
contemporaneous with the crisis in markets, at worst they spike
after crisis. Laura Kodres et al IMF WP /2013/115 now call market
based systemic risk indices Coincident and Near Coincident
Systemic Risk Measures: conceded absence of early warning
capabilities.
As credit growth boosts asset prices, CDS spreads and VIX indices
which are inversely related to asset prices are at their lowest precisely
before the crash when asset prices peak → Also procyclicality of
leverage Adrian and Shin (2010, 2011).

6. 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

7. “Paradox of stability” : Stock Index and Volatility Index Paradox of
Volatility (Borio and Drehman(2009); Minsky (1982)) Volatility low
during boom and at local minimum before market tanks : hence misled
regulators “great moderation”

8. IMF WP /2013/115 Market Data Based Systemic Risk Measures:
Coincident or Near Coincident Devoid of Early Warning Few Weeks at
Best
Arsov et. al. (2013) design IMF Systemic Financial Stress (SFS, black above)
index which records the extreme negative returns at 5 percentile of the (left) tail
for the joint distribution of returns of a selected sample of large US and Eurozone
FIs (Ibid Figure 4 ) Backtesting of popular systemic risk metrics (Red, above)

9. (ii) 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.
At the level of the individual user micro-prudential schemes appear
plausible but at the macro-level may lead to systemically unsustainable
outcomes.
Example 1 : Risk sharing in advanced economies uses O-T-C derivatives.
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 1.6% capital
charge if banks got CDS guarantees from ‘AAA’ providers

10. Structure of Global Financial Derivatives Market:Modern
Risk Management based on Fragile Topology that Mitigates
Social Usefulness (2009,Q4 204 participants): Green(Interest Rate),
Blue (Forex), Maroon ( Equity); Red (CDS); Yellow (Commodity); Circle 16
Broker Dealers in all markets (Source Markose IMF W, 2012)

11. Granular Banks and Non Bank Financial Intermediaries (Dec 2012)- Note that
insurance companies (H codes) mutual funds(G codes) and not banks (A-D
codes) are net liquidity providers: Fact can be missed in banks only models !

12. A Financial Intermediary is member of multiple financial
markets (multi-layer networks) How to calculate its
centrality across the different networks it is present ?Joint
Eigen-vector centrality
Multi-Layer Network with
common nodes in some
layers ; m markets
Single network

13. Castren and Racan (ECB 2012 WP) Phenomenal Global Macro-net
Model With National Sectoral Flow of Funds To Track Global Financial
Contagion! Only Problem- the Castren-Racan Systemic Risk Analytics
Fail to have Early Warning Capabilities
The circle in the center represents banking systems that are exposed to the cross
border liabilities of sectors (household, non bank corporate, public etc) within
countries. The latter with sectoral flow of funds are given in the outer circle

14. Castren-Racan (2012) Loss Multiplier Systemic Risk Measure(blue
lines) vs. Markose et al (2012, 2013) Maximum Eigenvalue of Matrix of
Net Liabilities Relative to Tier 1 Capital (green line)
Castren-Racan loss multiplier (blue lines), unfortunately, peaks well after crisis has
started and asset side of FIs is considerably weakened. Markose (2012,2013) direct
measure of maximum eigenvalue, (green line)of matrix of liabilities of countries relat
Tier1 capital of the exposed national banking systems, will capture growing instabili
network relative to distribution of capital buffers well ahead of actual crisis.

15. Global Macro-net plagued by within country
sectoral imbalances and global imbalances
only 8% of total lending for real investment
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%Other Financial Institutions
Secured Household (banks)
Secured Household (BSocs)
Unsecured Household
LBO targets
Commercial Real Estate
'core' PNFC

16. Network Stability and Systemic Risk Measure:
Why Does Network Structure Matter to Stability ?
lmax = 𝑁𝐶 s < 1 Formula for network stability
• My work influenced by Robert May (1972, 1974)
• Stability of a network system based on the
maximum eigenvalue lmax of an appropriate
dynamical system
• May gave a closed form solution for lmax in terms
of 3 network parameters , C : Connectivity , number
of nodes N and s Std Deviation of Node Strength :
lmax = 𝑁𝐶 s All 3 network statistics cannot
grow and the network remain stable. Eg a highly
asymmetric network with high s such as core periphery,
its connectivity has to be very low for it to be stable

17. From Epidemiology : Failure of i at q+1 determined
by the criteria that losses exceed a predetermined
buffer ratio, r, of Tier 1 capital
 𝑢 iq+1 = (1 - r) uiq +
(𝑥 𝑗𝑖−𝑥 𝑖𝑗)
𝐶 𝑖0
+
𝑢𝑗𝑞
1
𝑗 (2)
(i)First term i’s own survival probability given by the
capital Ciq it has remaining at q relative to initial capital
Ci0 , r is common cure rate and (1 - r) is rate of not
surviving in the worst case scenario .
(ii)The sum of ‘infection rates’= sum of net liabilities of
its j failed counterparties relative to its own capital is
given by the term
(𝑥 𝑗𝑖
−𝑥 𝑖𝑗
)
𝐶 𝑖0
+
𝑗

18. Stability of the dynamical network
system : Eigen Pair (λmax , v)
In matrix algebra dynamics of bank failures given by:
Ut +1 = [´ + (1- r)I] Ut = Q Ut (3)
I is identity matrix and r is the % buffer
 The system stability of (2) will be evaluated on the basis
of the power iteration of the matrix Q=[(1-r)I+Θ´]. From
(3), Uq takes the form:
Uq= Qq U0
 Stability Condition lmax(´) < r
After q iterations
λmax is maximum
eigenvalue of Θ

19. Solvency Contagion and Stability of Matrix Θ’
: Netted impact of i on j relative to j’s capital
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0...
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0
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1
11
33
3
3223
3
3113
2
2112
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jt
jNNj
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t
tt
C
xx
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C
xx

20. Financial network models to date have yielded mixed
results : None about propagators of 2007 crisis (C:
Core; P Periphery (see Fricke and Lux (2012))

21. Some Networks: A graphical representation of random
graph (left) and small world graph with hubs, Markose
et. al. 2004

22. 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)

23. Eigenvector Centrality (EVC)
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
l is maximum
eigenvalue of Θ
A variant is used in the Page Ranking algorithm used by Google
The vector v, containing centrality values of all nodes is obtained by solving the
eigenvalue equation Θ 𝒗 𝟏 = λmax 𝒗 𝟏.
λmax is a real positive number and the eigenvector 𝒗 𝟏 associated with the largest
eigenvalue has non-negative components by the Perron-Frobenius theorem (see
Meyer (2000))
Right Eigenvector Centrality : Systemic Risk Index Tax using Right EVC
Left Eigenvector centrality Leads to vulnerability Index

24. Mitigation of Systemic Risk Impact of
Network Central Banks: How to
stabilize ?
To date the problem of how to have banks internalize
their systemic risk costs to others (and tax payer) from
failure has not been adequately solved
In particular, penalty for being too interconnected has
not been dealt with from direct bilateral network data
Tax according to right eigenvector centrality

25. There are 5 ways in which stability of the
financial network can be achieved
(i)Constrain the bilateral exposure of financial
intermediaries (Ad hoc constraints do not work) Serafin
Martinez implemented these in Mexico
(ii) Ad hocly increase the threshold rho in (11),
(iii) Change the topology of the network
(iv) Directly deduct a eigenvector centrality based
prefunded buffer in matrix
Si
# = 𝜃𝑗𝑖
#
𝑗 =
1
𝐶 𝑖
( (𝑥𝑗𝑖𝑗 − 𝑥𝑖𝑗)+ −  vi 𝐶𝑖) .
(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

26. How to stabilize: Superspreader tax
quantified : tax using Eigen Vector Centrality
of each bank vi or vi ^2 to reduce max
eigenvalue of matrix to 6%

27. Superspreader tax rate

28. • 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. Knowledge of financial
interconnectivity essential for targeted interventions
• Highly connected nodes become infected first and
epidemic dying out fast and often contained in first two
tiers
• Innoculate a few rather than whole population;
Strengthen hub; Reduce variance of node strength in
maximum eigenvalue formula
Conclusion : Regulators and Systemic Risk Researchers must face up
to limits of data mining market price data for early warning signals and
instead mandate structural bilateral financial data and digitally map the
macro-financial network system

29. • Changes in eigenvector centrality of FIs can give
early warning of instability causing banks
• EVC basis of Bail in Escrow fund/Capital
Surcharge
• These banks with high Eigen vector centrality
will, like Northern Rock, be winning bank of the
year awards ; however potentially destabilizing
from macro-prudential perspective
Capital for CCPs to secure system stability can
use same calculations
• Beware gross aggregation and netting across
product classes for which there is no multi-lateral
clearing ; more systemic risk and hence more,
capital/collateral needed for stabilization
• Single network v multi-layer networks
Other Concluding Remarks

30. References:
(1) Markose, S.M (2013) "Systemic Risk Analytics: A Data
Driven Multi-Agent Financial Network (MAFN) Approach",
Journal of Banking Regulation , Vol.14, 3/4, p.285-305, Special
Issue on Regulatory Data and Systemic Risk Analytics.
(2) Markose, S. (2012) “Systemic Risk From Global Financial
Derivatives: A Network Analysis of Contagion and Its Mitigation With
Super-Spreader Tax”, November, IMF Working Paper No. 12/282,
(3) Markose, S., S. Giansante, and A. Shaghaghi, (2012), “Too
Interconnected To Fail Financial Network of U.S. CDS Market:
Topological Fragility and Systemic Risk”, Journal of Economic
Behavior and Organization, Volume 83, Issue 3, August 2012, P627-
646
http://www.sciencedirect.com/science/article/pii/S0167268112001254
(3)Multi-Agent Financial Network (MAFN) Model of US Collateralized
Debt Obligations (CDO): Regulatory Capital Arbitrage, Negative CDS
Carry Trade and Systemic Risk Analysis, Sheri M. Markose, Bewaji
Oluwasegun and Simone Giansante, Chapter in Simulation in
Computational Finance and Economics: Tools and Emerging
Applications Editor(s): Alexandrova-Kabadjova B., S. Martinez-
Jaramillo, A. L. Garcia-Almanza, E. Tsang, IGI Global, August 2012.
http://www.acefinmod.com/CDS1.html