Networks in finance

Just over a week ago, the journal Nature Physics published an unusual issue. In addition to the standard papers on technical physics topics, this issue contained a section with a special focus on finance, especially on complex networks in finance. I'm sure most readers of this blog won't have access to the papers in this issue, so I thought I'd give a brief summary of the papers here.

It's notable that these aren't papers written just by physicists, but represent the outcome of collaborations between physicists and a number of prominent economists (Nobel Prize winner Joseph Stiglitz among them) and several regulators from important central banks. The value of insight coming out of physics-inspired research into the collective dynamics of financial markets is really starting to be recognized by people who matter (even if most academic economists won't wake up to this probably for several decades).

I've written about this work in my most recent column for Bloomberg, which will be published on Sunday night EST. I was also planning to give here some further technical detail on one very important paper to which I referred in the Bloomberg article, but due to various other demands in the past few days I haven't quite managed that yet. The paper in question, I suspect, is unknown to almost all financial economists, but will, I hope, gain wide attention soon. It essentially demonstrates that the theorists' ideal of complete, arbitrage free markets in equilibrium isn't a nirvana of market efficiency, as is generally assumed. Examination of the dynamics of such a market, even within the neo-classical framework, shows that any approach to this efficient ideal also brings growing instability and likely market collapse. The ideal of complete markets, in other words, isn't something we should be aiming for. Here's some detail on that work from something I wrote in the past (see the paragraphs referring to the work of Matteo Marsili and colleagues).

Now, the Nature Physics special issue.

The first key paper is "Complex derivatives," by Stefano Battiston, Guido Caldarelli, Co-Pierre Georg, Robert May and Joseph Stiglitz. It begins by noting that the volume of derivatives outstanding fell briefly following the crisis of 2008, but is now increasing again. According to usual thinking in economics and finance, this growth of the market should be a good thing. If people are entering into these contacts, it must be for a reason, i.e. to hedge their risks or to exploit opportunities, and these deals should lead to beneficial economic exchange. But, as Battiston and colleagues note, this may not actually be true:

By engaging in a speculative derivatives market, players can potentially amplify their gains, which is arguably the most plausible explanation for the proliferation of derivatives in recent years. Needless to say, losses are also amplified. Unlike bets on, say, dice — where the chances of the outcome are not affected by the bet itself — the more market players bet on the default of a country, the more likely the default becomes. Eventually the game becomes a self-fulfilling prophecy, as in a bank run, where if each party believes that others will withdraw their money from the bank, it pays each to do so. More perversely, in some cases parties have incentives (and opportunities) to precipitate these events, by spreading rumours or by manipulating the prices on which the derivatives are contingent — a situation seen most recently in the London Interbank Offered Rate (LIBOR) affair.

Proponents of derivatives have long argued that these instruments help to stabilize markets by distributing risk, but it has been shown recently that in many situations risk sharing can also lead to instabilities.

The bulk of this paper is devoted to supporting this idea, examining several recent independent lines of research which indicate the more derivatives can make market less stable. This work shares some ideas with theoretical ecology, where it was once thought (40 years ago) that more complexity in an ecology should generally confer stability. Later work suggested instead that complexity (at least too much of it) tends to breed instability. According to a number of recent studies, the same seems to be true in finance:

It now seems that the proliferation of financial instruments induces strong fluctuations and instabilities for similar reasons. The basis for pricing complex derivatives makes several conventional assumptions that amount to the notion that trading activity does not feed back on the dynamical behaviour of markets. This idealized (and unrealistic) model can have the effect of masking potential instabilities in markets. A more detailed picture, taking into account the effects of individual trades on prices, reveals the onset of singularities as the number of financial instruments increases.

The remainder of the paper goes on to explore various means that may be taken, through regulations, to try to manage the complexity of the financial network and encourage its stability. Stability isn't something we should expect to occur on its own. It demands real attention to detail. Blind adherence to the idea that "more derivatives is good" is a recipe for trouble.

The second paper in the Nature Physics special issue is "Reconstructing a credit network," by Guido Caldarelli, Alessandro Chessa, Andrea Gabrielli, Fabio Pammolli and Michelangelo Puliga. This work addresses an issue that isn't quite as provocative as the value of the derivatives industry, but the topic may be of extreme importance in future efforts to devise effective financial regulations. The key insight coming from network science is that the architecture of a network -- its topology -- has a huge impact on how influences (such as financial distress) spread through the network. Hence, global network topology is intimately linked up with system stability; knowledge of global structure is absolutely essential to managing systemic risk. Unfortunately, the history of law and finance is such that much of the information that would be required to understand the real web of links between financial institutions remains private, hidden, unknown to the public or to regulators.

The best way to overcome this is certainly to make this information public. When  financial institutions undertake transactions among themselves, the rest of us are also influenced and our economic well being potentially put at risk. This information should be public knowledge, because it impacts upon financial stability, which is a public good. However, in the absence of new legislation to make this happen, regulators can right now turn to more sophisticated methods to help reconstruct a more complete picture of global financial networks, filling in the missing details. This paper, written by several key experts in this technical area, reviews what is now possible and how these methods might be best put to use by regulators in the near future.

Finally, the third paper in the Nature Physics special issue is "The power to control," by Marco Galbiati, Danilo Delpini and Stefano Battiston. "Control" is a word you rarely hear in the context of financial markets, I suppose because the near religion of the "free market" has made "control" seem like an idea of "communists" or at least "socialists" (whatever that means). But regulation of any sort, laws, institutions, even social norms and accepted practices, all of these represent some kind of "control" placed on individuals and firms in the aim, for society at large, of better outcomes. We need sensible control. How to achieve it?

Of course, "control" has a long history in engineering science where it is the focus of an extensive and quite successful "control theory." This paper reviews some recent work which has extended control theory to complex networks. One of the key questions is if the dynamics of large complex networks might be controlled, or at least strongly steered, by influencing only a small subset of the elements making up the network, and perhaps not even those that seem to be the most significant. This is, I think, clearly a promising area for further work. Let's take the insight of a century and more of control theory and ask if we can't use that to help prevent, or give early warnings of, the kinds of disasters that have hit finance in the past decade.

Much of the work in this special issue has originated out of a European research project with the code name FOC, which stands for, well, I'm not exactly sure what it stands for (the project describes itself as "Forecasting Financial Crises" which seems more like FFC to me). In any event, I know some of these people and apart from the serious science they have a nice sense of humor. Perhaps the acronym FOC was even chosen for another reason. As I recall, one of their early meetings a few years ago was announced as "Meet the FOCers." Humor in no way gets in the way of good science.