Tuesday, 2 April 2013


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.

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.

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 analysis not only 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[1]-- those institutions that present the greatest risks to the financial system are those that, if they fail, would cause the widest spread of economic distress. Naturally, you would tend to have a high DebtRank if you are linked by loans and other financial ties to other firms with high DebtRank -- the same circularity as PageRank,  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"[2] by Marco Galbiati, Danilo Delpini & Stefano Battiston     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.

TARGET2 Represented as a bow-tie diagram
This network has 691 nodes (not all represented for the sake of clarity). The higher a node's feedback centrality, the closer it is to the centre of the spiral of the strongly connected component (SCC), and the larger its size. The nodes in the top box represent participants from which liquidity moves out but does not enter, those in the lower right box receive liquidity but do not transfer it back. Some nodes act as drivers (red); others don't (green). Links between nodes within the SCC are colour-scaled from yellow to green; links from a small set of liquidity providers (top) to the SCC are shown in orange; and links from the SCC to a large set of liquidity receivers (lower right) are grey. In all cases, the darker the hue, the higher the degree of the node that the link originates from.

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.

Transactions of the Italian electronic interbank market e-MID

The average degree of driver banks (red line, left-hand axis) is systematically lower than the average degree of the network (blue line, left-hand axis). Moreover, the percentage of top lender banks that are also drivers (green line, right-hand axis) is well below 100%, but rises significantly at the onset of the global financial crisis in 2008.

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". However, methods[3] can be developed 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. There are many incentives at work for market players to engage in an intricate web of complex derivative contracts that, overall 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 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 analysis seems a precondition for trying and understanding the positive feedbacks that are at play in this complex system.

The largest players in the derivatives market.
Despite a downturn following the 2008 financial crisis, the volume of derivative contracts for 30 top market players continues to increase, with the 7 biggest labelled in colour.

In this respect,  Michele Catanzaro & Mark Buchanan[4] argue 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)[5] 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.

[1] Stefano Battiston,  Michelangelo Puliga, Rahul Kaushik, Paolo Tasca & Guido Caldarelli.
"DebtRank: Too Central to Fail? Financial Networks, the FED and Systemic Risk", Scientific Reports
[2] "The power to control" Marco Galbiati, Danilo Delpini & Stefano Battiston, Nature Physics
[3] "Reconstructing a credit network" Guido Caldarelli, Alessandro Chessa, Fabio Pammolli, Andrea Gabrielli & Michelangelo Puliga
[4] "Network opportunity" Michele Catanzaro & Mark Buchanan
[5] http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/dsges.html
[6] "Complex derivatives" Stefano Battiston, Guido Caldarelli, Co-Pierre Georg, Robert May & Joseph Stiglitz

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