Main menu

Nature Physics FOCUS on financial networks


Nature Physics Focus issue: March 2013 Volume 9, No 3 pp119-197




The financial crisis has made us aware that financial markets are very complex

networks that, in many cases, we do not really understand and that can easily go

out of control. This idea, which would have been shocking only 5 years ago, results

from a number of precise reasons. In this Focus, for the first time, network scientists,

economists and regulators team-up to discuss for a wider audience the fundamental

challenges posed by complex financial networks to the stability of our economies. The

Focus consists of four interconnected papers that: offer some intuition of why financial

networks can get so complex and unstable; provide examples of the new network

approaches that are currently pursued by regulators; and indicate research avenues that

should to be explored in the future.


The Focus represents an important outcome of the work carried out in the European

project FOC ( that deals with alternative methods to model

economic complexity and financial crises. Two of the papers have also been supported

by the Institute of New Economic Thinking.


Overall, the arguments and the findings presented in the Focus could be roughly

summarized as follows. Systemic risk is not a remote event but a typical situation of

financial networks let on their own dynamics. Systemic risk is an emerging property,

an externality in the economic jargon, that arises from the complex interaction of the

private economic interests of market players. More data and more network science can

help us shaping institutions and markets that are better suited for the good of society

at large. However, financial regulation is of little effect if the economic influence of big

market players is not seriously addressed.


The authors include the Nobel prize for economics Joseph Stiglitz, the mathematician

and ecologist Lord Robert May, a representative of the Bank of England and former

European Central Bank adviser (Marco Galbiati), a representative of the Deutsche

Bundesbank (Co-Pierre Georg), and the two founders of the FOC project (Guido

Caldarelli and Stefano Battiston). The other authors include both economists and



More details.

In more detail, the four papers can be outlined as follows.


Many portions of the financial system can be thought of as networks in which financial

institutions are the nodes and financial contracts such as loans or derivatives are the

links. Links are in general directed and weighted as they can associated for instance

with the value of the contract. Network science provides statistics to describe the overall

network structure (i.e. the distribution of the number of links or the modularity that

measures the organization in communities) but also measures to assess the importance

of individual nodes according to certain criteria. The algorithm DebtRank, cited several

times in the Focus represents a successful example of a method recently introduced to

overcome the limitations of the state of the art. It includes network effects that were

previously neglected in the propagation of distress and it is currently being tested by

researchers at various central banks.


The paper "The power to control" explains how the two different notions of centrality

and controllability can be applied to concrete case studies. In particular, the paper

reports the results of one of the first network analysis of the TARGET2 infrastructure

for large payments in Europe. It is shown how the nodes that drive the system are not

necessarily the hubs or those responsible for the largest volumes of transactions. In a

nutshell, in a network, due the multiple chains if connections, it often happens that a

small cog is able to move a large cog. These notions are useful to devise concrete ways in

which regulators can try and control the well-functioning of certain markets.


However, one of the issues with financial networks is that often the structure is

unknown due to confidentiality issues. Indeed, it is in the interest of individual

institutions to keep their financial contracts undisclosed. This however prevents

the regulator to assess precisely the systemic risk, which depends critically on the

overall structure of the network. The error in the estimation is a sort of "social price of

private confidentiality". The paper "Reconstructing a credit network" sketches some

of the methods that have been recently developed in order to deal with this problem.

It is possible to estimate the macroscopic characteristics of a network as well as its

resilience starting from limited information on the existing links. It is also possible to

estimate financial interdependence based on time series of certain market indices such

as the spread of credit default swaps associated to a given institution. These methods

will hopefully contribute to building more reliable Early Warning Systems that detect

the building up of financial instabilities.


The bad news is that even if certain properties of network structures can be estimated

from partial information or from market indices time series, a more fundamental

issue lures at regulators from behind the scenes. As outlined in the paper “Complex

derivatives”, there are many incentives at work for market players to engage in an

intricate web of complex derivative contracts that, overall is constitutes in itself a

too-big-to-fail entity that will always be rescued at the with public money. Because

derivative contracts essentially amplify gain and losses and because they can depend

on the financial health of other agents in the network, the resulting system is highly

non-linear and intrinsically unstable. We are not even yet able to model the dynamics

of its components and certainly very far from being able to predict anything of its

global dynamics. In a nutshell, one possible view here is that derivatives, although

can be used to hedge risks, are actually many times used to take excessive risk at the

expenses of society at large, thus raising a serious moral hazard issue. The challenge for

regulators is really formidable here. Network science seems a precondition for trying

and understanding the positive feedbacks that are at play in this complex system.


In this respect, the paper “Network opportunities” argues that the problem of the

economic discipline so far has been precisely not to be able to deal with these positive

feedbacks. For various reasons, both the econometric approach and the so-called

Stochastic Dynamic General Equilibrium (SDGE) approach are essentially linear and

unable to model the instabilities and regime shifts that financial markets display so

often. It is clear that better science alone will not resolve economic crises, nor it will

allow the precise prediction of the economic or financial future. Certainly, however it is

seems to provide genuinely new and promising tools to help regulators and economists

to understand and mitigate systemic risk.