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

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)

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.

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

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).

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

“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”

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)

(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

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)

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 !

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

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

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 relative to

Tier1 capital of the exposed national banking systems, will capture growing instability of

network relative to distribution of capital buffers well ahead of actual crisis.

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

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

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 + (𝑥𝑗𝑖−𝑥𝑖𝑗)

𝐶𝑖0

+

𝑢𝑗𝑞1

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 (𝑥𝑗𝑖

−𝑥𝑖𝑗

)

𝐶𝑖0

+

𝑗

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

Solvency Contagion and Stability of Matrix Θ’

: Netted impact of i on j relative to j’s capital

)2(

0...)(

....)(

.0........

)(...0....

)(.........0..

)(........

)(00

0.....0.)()(

0

1

11

1

11

33

3

3223

3

3113

2

2112

jt

jNNj

t

NN

Nt

NiiN

t

ii

Nt

NN

t

tt

C

xx

C

xx

C

xx

C

xx

C

xx

C

xx

C

xx

C

xx

Financial network models to date have yielded mixed

results : None about propagators of 2007 crisis (C:

Core; P Periphery (see Fricke and Lux (2012))

Some Networks: A graphical representation of random

graph (left) and small world graph with hubs, Markose

et. al. 2004

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)

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 𝒗𝟏 = λmax 𝒗𝟏 .

λmax is a real positive number and the eigenvector 𝒗𝟏 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

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

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

𝐶𝑖 ( (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

exogenously.

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%

Superspreader tax rate

• 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

• 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

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