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This is just an illustration of how and economic systems, with an attendant Michele Catanzaro and Mark Buchanan are information technology can help in increase in our capacity to manage them and freelance science writers. quantifying subtle collective behaviours. In avoid the worst problems. One important e-mails: [email protected]; the context of , such experiments challenge, among many others, is to make [email protected] could be enormously valuable. For example, scientific advances both available to the it has been shown11 that the volume of public, and useful for policymakers. No References transactions of a at a certain time is one believes that better science alone will 1. Kirman, A. Riv. Ital. Econ. 16, 9–36 (2011). 2. Buchanan, M. Nature 460, 680–682 (2009). correlated to the volume of searches related make economic crises a thing of the past, or 3. http://www.ecb.int/press/key/date/2010/html/sp101118.en.html to that company at the previous time-step — allow the precise prediction of the economic 4. Caldarelli, G. & Cantanzaro, M. Networks: A Very the reason is unclear, but it could be that the or financial future. But better models that Introduction (Oxford Univ. Press, 2012). 5. http://www.bankofengland.co.uk/publications/Documents/ number of searches is a rough measure of the take into account feedbacks and network speeches/2009/speech386.pdf (generated by worry or enthusiasm) dynamics should greatly boost the ability of 6. Battiston, S., Puliga, M., Kaushik, R., Tasca, P. & Caldarelli G. in that company. Notably, similar systems everyone to foresee the kinds of events to Sci. Rep. 2, 541 (2012). have been employed to predict other which markets and are prone, 7. Vitali, S., Glattfelder, J. B. & Battiston, S. PLoS ONE 6, e25995 (2011). 8. Battiston, S., Delli Gatti, D., Gallegati, M., Greenwald, B. C. & 12 phenomena, such as flu epidemics . to understand the conditions that are likely Stiglitz, J. E. J. Econ. Dynam. Contr. 36, 1121–1141 (2012). The coincidence of new theoretical tools, to create them, and to offer some guidance 9. Thurner, S., Farmer, J. D. & Geanakoplos, J. Quant. Finance a wealth of new data and the will to change on how to avoid those circumstances. 12, 695–707 (2012). 10. , R. M. et al. Nature 489, 295–298 (2012). paradigms provides a chance for a leap Even a little more knowledge could be of 11. Bordino, I. et al. PLoS ONE 7, e40014 (2012). forward in our understanding of financial great . ❐ 12. Ginzberg, J. et al. Nature 457, 1012–1014 (2009). Complex derivatives Stefano Battiston, Guido Caldarelli, Co-Pierre Georg, Robert May and Joseph Stiglitz The intrinsic complexity of the financial derivatives has emerged as both an incentive to engage in it, and a key source of its inherent instability. Regulators now faced with the challenge of taming this beast may find inspiration in the budding science of complex systems.

hen financial derivatives were By engaging in a speculative derivatives are not affected by the bet itself — the cast1 in 2002 as latent ‘weapons market, players can potentially amplify more market players bet on the of a Wof mass destruction’, one might their gains, which is arguably the most country, the more likely the default becomes. have expected the world at large to sit up plausible explanation for the proliferation of Eventually the game becomes a self-fulfilling and listen — particularly in the wake of derivatives in recent years. Needless to say, prophecy, as in a run, where if each subsequent events that led to the financial losses are also amplified. Unlike bets on, say, party believes that others will withdraw their crisis of 2008. Instead, the derivatives dice — where the chances of the outcome from the bank, it pays each to do so. market continues to grow in size and More perversely, in some cases parties have complexity (Fig. 1), spawning a new incentives (and opportunities) to precipitate generation of financial innovations, and these events, by spreading rumours or raising concerns about its potential impact 1.5 by manipulating the on which the on the as a whole. derivatives are contingent — a situation ) A instrument is a financial Deutsche seen most recently in the London Interbank contract between two parties, in which Bank Offered Rate (LIBOR) affair. 1.0 the value of the payoff is derived from Barclays Proponents of derivatives have es (millions the value of another RBS argued that these instruments help to ativ or , called the underlying entity. In UBS AG stabilize markets by distributing , some cases, this contract acts as a kind Deriv 0.5 BNP but it has been shown recently that in of : in a default , for Paribas many situations risk sharing can also lead example, a lender might buy protection HSBC to instabilities2,3. from a third party to insure against the default of the borrower. However, unlike 2005 2010 Market as network conventional insurance, in which a person Year Players engaging in the necessarily owns the house she wants can enter into an unlimited number of to insure, derivatives can be negotiated Figure 1 | The largest players in the derivatives contracts with other parties, so the market on any underlying entity — meaning market. Despite a downturn following the 2008 can be seen as a complex financial network, anyone could take out insurance on the , the volume of derivative contracts in which interactions between the nodes house in question. therefore for 30 top market players continues to increase, are nonlinear4. A derivative contract can emerges as another reason to with the 7 biggest labelled in colour. Data from itself be made arbitrarily complex — it has in derivatives. Bankscope © 2013 Bureau van Dijk. been estimated5 that if one of these contracts

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were presented in the older idiom of a This makes it harder to estimate the risk fact that increasing complexity in a network ‘’, it could run to something like of the deal, resulting in an information inevitably leads to its destabilization. One 109 pages. Derivatives can be constructed asymmetry that can be exploited at the might think of this as a formalization of the recursively, such that one derivative of other parties. In markets with everyday idea that complicating matters underlies another, and the payoff can depend full rationality, such contracts wouldn’t be tends to multiply the number of ways that on any imaginable set of events — say, the executed — the party with less information things can go wrong. weather in London three months from now. would simply refuse to sign6. But there is It now seems that the proliferation This means that in modelling the market ample evidence in the literature of both of financial instruments induces strong as a network, representing as nodes economics and psychology to suggest fluctuations and instabilities for similar and contracts as links, one quickly finds that that individuals routinely overestimate reasons4. The basis for pricing complex both nodes and links can depend on the state their own knowledge. derivatives makes several conventional of other nodes in the network. This requires Another way that financial institutions assumptions that amount to the notion building an extra level of complexity into the profit from complexity stems from their need that trading activity does not feed back on network models with which physicists have to be perceived as systemically important, to the dynamical behaviour of markets. This become familiar. Describing the dynamics guarantee governmental rescue in the face idealized (and unrealistic) model can have of such a system is enough of a challenge for of crisis. Systemic importance is no longer the effect of masking potential instabilities in network science — apart from the problems regarded as simply a matter of size — of markets. A more detailed picture, taking into posed by predicting its behaviour and banks being ‘’. In complex account the effects of individual on ensuring its robustness to failure. networks, an initial impact can be greatly prices, reveals the onset of singularities as the The network is further complicated by a amplified by cascading along the network’s number of financial instruments increases4. lack of transparency. A large fraction of trades connections. A correspondence between The continued development of myriad new on the derivatives network occur over-the- cascade sizes and ‘centrality’ — quantifying instruments and the steady increase in the counter (OTC), meaning they are privately a node’s importance in the network — has number and connectivity of market players negotiated between two parties without the therefore given rise to the idea of a bank therefore seem to give rise to the conditions need for an intermediary. Worldwide, the being ‘too central to fail’, which can be stipulated by the May–Wigner theorem. total volume of OTC derivatives increased captured by the DebtRank indicator7. Related The instability is not necessarily easy to steadily from US$100 trillion in 2000 to over notions of ‘too connected to fail’ or ‘too understand from the idealized model. The US$500 trillion in 2011 — more than five correlated to fail’ are also now beginning to idea is that once there are enough derivative times the global gross domestic product. be factored into governmental subsidization instruments available to meet the demands Despite the huge volumes involved, all of the financial sector. of all players, the market is essentially OTC contracts are confidential and are not But the perceived benefits of complexity complete. But as long as there is a monetary disclosed, rendering the structure of the are certainly not restricted to the network incentive to create new instruments, banks network largely obscure — and hindering players that fulfil these key roles. The will continue to do so. Subsequent trades will our understanding of the derivatives complexity of both the instruments and the then serve only to increase the complexity market as a complex system. Indeed, these network structure can render peripheral of the network at the expense of stability. characteristics make the market vulnerable institutions virtually indistinguishable from The irony is that if the market were in fact to the build-up of instabilities that suddenly, the core of institutions that are guaranteed complete, these contracts would have no real and unpredictably, induce cascades of the subsidy — meaning that risk- effect. But under the real-world conditions sort shared by many nonlinear phenomena averse will also come to their of an incomplete market characterized by in physics. rescue. If the market were more transparent, considerable complexity, these trades, even The European Commission has recently would be stronger, and profits if individually rational, may undermine adopted new reporting standards that may would be eroded. Thus, being ‘too complex systemic market performance. improve the situation, and could be enforced to fail’ may pay off well for individual banks, On the other hand, ensuring a diversity of as early as the end of 2013. Without such even if it undermines systemic performance. players and restricting the scope of measures, this lack of transparency may And there remains an even less savoury in which they can engage may emerge, we itself contribute to an intrinsic financial use of complexity. Derivatives can be used believe, as one of the few ways of limiting instability, setting aside the problems to manipulate accounts to make things the incentives of market participants to associated with regulators having restricted seem better at one moment, at the cost of engage in highly correlated behaviour — a access to information. Indeed, when market making things look worse at another. The practice that would otherwise lead naturally participants come to believe that there are most notorious example of this is a recent to . large asymmetries of information, they may case of financial institutions using derivatives not trade with each other. This so-called to make Greece’s financial Regulate to accumulate no-trade theorem6 — sometimes referred appear strong enough for membership of The fact that derivatives may not only to as a drying up of liquidity—is precisely the Eurozone. hamper the assessment of systemic risk, what happened in 2007–2008: the interbank but also foster its emergence, has spurred lending market dried up, and banks refused Complexity and instability a debate in recent years about the global to lend to each other, forming a key factor in Early studies of ecosystem stability financial architecture and its possible prompting the global financial crisis. erroneously implied that greater regulation. Four key reforms have been Paradoxically, this information complexity — given by more species proposed, emphasizing the need for asymmetry is one of the main incentives for interacting more extensively — automatically transparency and exchange markets, market players to engage in a derivatives conferred greater robustness. But subsequent targeting the implicit subsidies that market that is so complex. Derivatives, investigation has shown that, in general, the government-insured entities receive from especially OTC derivatives, are not easy to converse is true. This is encapsulated by the the public and removing the priority given to , and their evaluation relies on models. May–Wigner theorem8, which conveys the derivative instruments in bankruptcy.

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Enforcing the use of exchange markets important role in limiting the development am Main, Germany, 5Oxford University, will make information on prices, volumes of regulatory structures designed to enhance Oxford OX1 1HP, UK and 6Columbia and exposures available to regulators and the systemic stability. In any case, reform must be University, New York 10027, USA. public — rendering the network structure approached dynamically, as market players — *e-mail: [email protected] more transparent. It is also likely to limit the pursuing their individual incentives — find intrinsic problems associated with network ever new ways to circumvent existing References 1. Buffett, W. E. Letter to Shareholders 2002 (Berkshire Hathaway interdependence, because the failure of regulations at the expense of systemic Inc., 2002); available at http://www.berkshirehathaway.com/ an individual party would be absorbed by stability and social welfare. letters/2002pdf.pdf the exchange market, rather than being This certainly amounts to a formidable 2. Stiglitz, J. E. Am. Econ. Rev. 100, 388–392 (2010). transmitted through the network. However, challenge, from the point of view of both 3. Battiston, S., Gatti, D. D., Gallegati, M., Greenwald, B. C. N. & Stiglitz, J. E. J. Econ. Dyn. Contr. 36, 1121–1141 (2012). these markets, if undercapitalized, could also network science and political economy 4. Haldane, A. G. & May, R. M. Nature 469, 351–355 (2011). lead to a heightened systemic risk. theory, with significant societal implications. 5. Corrigan, E. G. Structure: A Longer View. In general, well-designed regulatory Clearly, the development of new network- ( Bank of New York, 1987). 6. Stiglitz, J. E. in : Essays in Honor of systems must focus simultaneously based metrics to assess systemic risk Paul Cootner (eds Sharpe, W. F. & Cootner, C. M.) 118–158 on regulating the derivatives network, and evaluate the importance of financial (Prentice Hall, 1982). and mediating the influence of market institutions will be of enormous value — 7. Battiston, S., Puliga, M., Kaushik, R., Tasca, P. & Caldarelli, G. Sci. Rep. 2, 541 (2012). participants on future policies. It is clear forging an already promising union 8. May, R. M. Nature 238, 413–414 (1972). that banks profit from being regarded as too between , network scientists connected, too correlated — and even too and regulators. ❐ Acknowledgements complex — to fail, giving them an incentive The authors acknowledge support from the European 1 2,3 FET Open Project FOC ‘ Financial Crises’ to engage in excessive risk taking and Stefano Battiston * Guido Caldarelli (No. 255987) and from the Working Group on Networks 4,5 5 amplifying the degree of systemic instability. Co-Pierre Georg Robert May and and Systemic risk, part of the Institute for New Economic A prudent strategy would therefore not Joseph Stiglitz 6 are at 1ETH Zürich, 8092 Thinking’s Financial Stability Research Program. only tame interdependencies and risk Zurich, Switzerland, 2IMT Alti Studi Lucca, 3 Disclaimer taking, but also restrict the power of the 55100 Lucca, Italy, London Institute for The views expressed in this Commentary do not necessarily financial sector. Unfortunately, lobbying Mathematical Sciences, London W1K 2XF, UK, reflect the views of Deutsche Bundesbank or the European has played — and continues to play — an 4Deutsche Bundesbank, D-60431 Frankfurt System of Central Banks. Reconstructing a credit network Guido Caldarelli, Alessandro Chessa, Andrea Gabrielli, Fabio Pammolli and Michelangelo Puliga The science of complex networks can be usefully applied in finance, although there is limited data available with which to develop our understanding. All is not lost, however: ideas from statistical physics make it possible to reconstruct details of a financial network from partial sets of information.

etween financial systems or agents with a corresponding increase of , developed during the current financial crisis, there may be reciprocal ties, of irregular and risk shifting, liquidity from bailouts to asset purchase programmes. Bnumber and weight, which create a evaporation, collateral shortages and so on5. Furthermore, when evaluating systemic risk highly connected structure with the features Given that a network’s diffusion for a specific , we must of a complex network1–4 — those ties may be properties are deeply entwined with its also consider the kind of ties it has, be they in the form of liability, exposure, ownership topology, it is crucial to focus on the precise lending, exposure, correlation or ownership. or simple correlation. Together these factors structure of the network. For example, Some ties result in more stable configurations describe a topology for which the diffusion even a few randomly placed shortcuts on a than others, and this multilevel structure — dynamics — of information, or of financial regular grid can create the so-called small- which lacks an adequate mathematical distress — among the institutions, or nodes, world effect — a radical reduction of the representation at present— allows distress of the network is not straightforward, and distances between regions of the system that to propagate in environments that otherwise can be quite unexpected. are otherwise far apart — which is one of seem solid. Distress propagating in a financial network the main reasons for the surprising velocity can cause bankruptcies and spread distrust, of distress propagation. It is therefore of Missing links thereby changing the shape and the topology fundamental importance to know how much Despite all that could be learned from an of connections. This in turn can give rise to a the results of any analysis depend on exact evaluation of systemic risk from topology, self-sustained process of failures, in an often- knowledge of the network structure. there is a major problem: lack of relevant unstoppable domino effect. In such a context, The network structure of financial information. Regulators, network scientists risk exposure is affected not only by the systems is central to many of the processes and economists are trying to get access quality of an institution’s counterparts, but also and mechanisms that come into play during to data on financial institutions that are by the quality of many other players, through a crisis, and it has become a key motivation confidential at present. At the same time, complex chains of actions and reactions and for some of the ‘macroprudential’ policies6 they are trying to find the best way to merge

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