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Culture, history and society

Culture, history and society

Econophysicists find a forum

02 Sep 1999

Over the past decade, banks and financial institutions have been hiring physicists and mathematicians with PhDs on a large scale. At one time, according to an article in The Economist in 1993, most of the scientists working in the field of finance were a bit embarrassed to be caught rubbing shoulders with mammon. But times have changed, and in mid-July the European Physical Society held its first conference on the applications of physics to financial analysis in Dublin.

The meeting gave the pioneers of “econophysics”, such as Jean-Phillippe Bouchard, János Kertész, Rosario Mantegna and Eugene Stanley, an official forum to present and debate their research on some of the most fascinating dynamical systems. The search for a scientific model that can accurately predict future movements in the financial markets is the investor’s equivalent of the quest for the holy grail. And physicists are now increasingly involved in this pursuit.

In Dublin 187 delegates gathered for two days to listen to 32 presentations and study 55 posters. These numbers illustrate the wide interest in the field among physicists in both academia and the finance industry. Indeed, the availability of financial data has spawned many empirical studies to which physicists bring new techniques and insight. These range from fractals and hydrodynamics to the Ising model of atomic spins in magnetic alloys.

The conference was dominated by two main approaches: the exploration of empirical regularities of financial data, and the numerical modelling of markets. The latter is mainly inspired by game theory – which looks at the way in which decisions influence economic gains and losses – and, in particular, the work of Brian Arthur of the Santa Fe Institute in the US. He devised a model known as the El Faro bar problem in which a large number of customers compete for a small number of seats in a bar. Indeed this type of problem, where scarce resources are allocated and managed, is the crux of economics. Now Damien Challet and Yi-Cheng Zhang from the University of Fribourg in Switzerland have reformulated the model and suggested improvements that will make it easier to implement.

The aim of many physicists working in this field is to develop statistical models that predict the probability that the price of stocks or shares will go up or down. Properties like the distribution of extreme events, such as stock-market crashes, and scaling behaviour have been explored with very large sets of high-frequency data. For instance, Luis Amaral of Boston University in the US reported results on the behaviour of about 40 million equity returns from the New York Stock Exchange. In simple terms, he compared how fluctuations in the prices of stocks and shares compared with a Gaussian distribution. His results confirm that financial assets are definitely riskier than the Gaussian random-walk behaviour would predict. Similar results have been found from studies of the foreign exchange market by Casper de Vries at the Tinbergen Institute in the Netherlands and the Olsen & Associates group in Zurich.

Rosario Mantegna from the University of Palermo in Italy showed that the relation between stock indices in different markets is remarkably stable over time. Such behaviour indicates that this correlation has a strong information content.

Meanwhile, Jean-Philippe Bouchaud, from Science & Finance in Paris, presented a study of interest rates and how they vary with the maturity of a loan. The interest rate that a customer is charged when they borrow money for one year is not the same as that charged to customers who borrow for 10 years. Yet the rates are not completely independent and a plot of the interest rate versus the maturity of the loan forms a so-called yield curve. Understanding the dynamics of this curve represents a real challenge. Currently the models that attempt to do so are rather crude and do not fit the data very well. Some inspiration from string theory could help here. (For more details on Bouchard’s work see Physics World January 1999.)

Eugene Stanley of Boston University explained how statistical physics could contribute to the science of economics. In particular, he extended his earlier work with Mantegna on the scaling behaviour of stock indices (Nature 1996 383 587). In finance, the time interval over which returns are measured constitutes a “fundamental” variable. In other words, the size of the return scales with the length of time over which an investment is made. Several groups have studied this behaviour since Mandelbrot’s work on cotton prices. In the early 1990s Olsen & Associates examined foreign exchange rates and interest rates, while Stanley’s group considered stock indices. All of these studies concur that financial returns cannot be viewed as a random walk.

Doyne Farmer, one of the founders of the Prediction Company – a private firm that conducts research into financial markets – gave the first talk of the conference. After several years working in the development of automatic trading systems and studying financial markets, Farmer has developed a model of the market that was inspired by evolutionary models in ecology. Farmer has formulated a theoretical framework that attempts to encompass both short and long evolutionary timescales. One of the main ideas of Farmer’s model is to define the rules for setting the price of goods according to supply and demand, and then study the evolution of different trading strategies given these rules. His model shows some interesting characteristics, like outbursts – where the volatility of a price rises well above its average value – and long oscillations, similar to those observed in the market.

Wolfgang Breymann of the University of Basel in Switzerland has extended his so-called information-cascade model, which made it possible to study market dynamics on a short timescale (S Ghashghaie et al. 1996 Nature 381 767). Now the model can reproduce the volatility of the stock market over longer periods. It assumes that events can happen at different timescales representing the trading behaviour of different market players.

In general, the most successful attempts to model financial markets account for the fact that the various market players have different strategies and attitudes to risk. At a given point in time, therefore, the different players have different opinions on whether to buy or sell. The success of such models has been confirmed by various research, including that of Neil Johnson from Oxford University and Giulia Iori from Essex University, both in the UK. These findings agree with recent developments in mainstream finance, thereby building a bridge between it and the econophysics approach.

Olsen & Associates presented a scale of market shocks, inspired by the Richter scale in geophysics, for quantifying market crises (see right). The idea is to be able to compare and analyse shocks in financial markets and monitor them continuously. Our model calculates the price movement from foreign exchange rates in terms of a scale that is related to the probability of a volatile occurrence. This scale is currently running at our offices and detects turbulence as it occurs. In a study of 1997 data, we were able to demonstrate the relative impact of the Asian crisis on the $/yen and the $/DM foreign exchange rates. We found that the latter was much more stable than the former, as expected. This is a first step towards building a global “early warning system” for financial crises.

Marcel Ausloos and Nicolas Vandewalle from the University of Liège in Belgium have been looking into similar problems. They used their experience in studying rupture phenomena in disordered materials to propose a method that attempts to predict the occurrence of financial crashes.

Some talks at the conference were more oriented towards economic theory. Per Bak from the Niels Bohr Institute in Copenhagen talked about the dynamics of money. He showed that the problem could be treated as a many-body dynamical system where the value of money in equilibrium is not fixed by equations and thus represents a “continuous symmetry”. Yi-Cheng Zhang from the University of Fribourg spoke about a new approach to efficient-market theory. In traditional efficient-market theory, the price of stocks and shares is impossible to predict because it follows a Gaussian random walk. Zhang’s approach, which is based on game theory, allows speculators to exploit inefficiencies of the system and thus make it efficient.

The diversity of the presentations in Dublin is a sign of the vitality of this new research field for physicists. Yet for it to prosper the organizers must seek closer links both to practitioners in the field (which should not be difficult given the number of physicists now working in banks) and to mainstream economists and finance researchers. There is no doubt that both groups would benefit from this interaction.

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