EUROPHYSIC NOTES 35 market it is this difference between the model builders select slightly different One Hundred Years of Gaussian fluctuations and the Levy fluctu­ aspects of trading. Physics in Finance ations.’ Solomon himself built a model in 1994 It has a longer history than you might ‘The next person to try and bring the in which traders have different memory expect.‘It is not even very modern,’ says hard sciences into the soft was Zipf in the spans, and so assess price changes over Sorin Solomon of econophysics. Solomon 20s and 30s. He was a professor at different periods. is a theoretical physicist at the Hebrew Princeton. He got very excited about pop­ Didier Sornette, at Nice University, con­ University, Jerusalem, but knows a thing ulations of towns which are distributed structed last year a hierarchical model of or two about stock markets.‘Exactly one- according to power laws,’ Solomon says. traders who imitate their superiors. hundred years ago in 1897 a French-born Power laws are different from exponen­ Professor Sornette, however, has done engineer, Pareto, wrote a book about eco­ tial laws which, for instance, describe the more than just build computer models. nomics in which the declared objective distribution of energies in a gas.‘There is According to Zhang: ‘Didier Sornette is was to transform economics into some­ a simple way to express the difference involved in making financial tools: how to thing like a physical science. This was the between typical physical systems and the make profit. He is successful in marketing first time someone took seriously the suc­ economic system which is the origin of his methods. He may never publish a com­ cesses of physics and tried to carry them the difference between power laws and plete history of his theories because there over into economics,’ Solomon explains. exponential laws,’ explains Solomon. is real money involved in his trading Solomon is drawn to stock markets ‘When molecules change their energy, strategies.’ because like many econophysicists he has they can loose or gain a quantum of ener­ Sornette is one example of a physicist found you can apply the statistical gy. When a person gains or looses on the prepared to put his money where his the­ mechanics of critical systems: ‘If you have stock market, they gain or loose a fraction ories are: with a colleague he bet on the a complex system, most of the time it is of their investment.’ market crash of last October, and made because there are very many elements (Recently, econophysicists have found 500 per cent profit. This, naturally, raises interacting by rather simple laws. And the that distributions of variations in market the question: will econophysicists soon be complexity comes just because there are prices fit a power law truncated by an leaving their physics departments head­ so many - emergent properties arise.’ exponential at short time scales, less than ing for the trading floor? In econophysics, you assume that a one day, and look more like a Gaussian at It’s known to be a possibility; and it’s complex price history arises because there monthly time scales and longer.) most likely, according to many econo­ are very many traders interacting by In the 1960s, power laws turned into physicists, to involve betting on the short­ rather simple rules. According to econo­ fractals, which in a sense are geometrical term volatility of a market, by trading physicists, the behaviour of prices expressions of power distributions. options, for example. emerges from the interactions between ‘Without Mandelbrot much of these However, Marcel Ausloos, Université de traders, like the pressure of a gas emerg­ things would have been forgotten,’ says Liege, Belgium, who made an appearance ing from the interactions of molecules. Solomon. But the field really opened up to on Belgium television last year because he Pareto, one hundred years ago, foresaw physicists with Kenneth Wilson’s work. also predicted last October’s crash, thinks that physics could be useful in trying to Kenneth Wilson, who the Nobel prize that physicists like himself are not likely understand the stock market. But, lacking for physics in 1982, said: ‘For a very wide to make much money - the predictions a computer, he was restricted by the range of microscopic interactions, if they are short term so riches will be earned approximations that limited the work of share the same general symmetry proper­ only by wealthy and powerful brokers. all physicists of the time. ties they will eventually have macroscopic But anyhow, econophysics is not for ‘Then in 1900 a thesis by Bachelier was interactions which are identical,’ explains those who like a quiet life. Different mod­ essentially the statistical mechanics of Solomon.‘This gave us the courage to go els are always hotly debated. And often stock markets.’ Solomon continues.‘At the to systems of economics. You can not hotly denounced by economists. same time there was another French pro­ enter in the mind of each of the persons Dietrich Stauffer, at Köln University, is fessor, Paul Levy. He was considered a lit­ who deals on the stock market and under­ currently writing a review called Non- tle bit of a crackpot, but eventually got a stand what he does there. But these very Traditional Applications of Comp­ professorship. He made quite good powerful techniques in statistical utational Statistical Physics, which he progress in mathematical distributions, mechanics and field theory guarantee to hopes to publish next year; it ranges from which turn out to be relevant for the stocl you that in certain conditions the macro­ bird song to immunology, and one chap­ market.’ scopic properties are independent of ter covers financial models. Zhang: ‘One Fluctuations in stock prices are not wel some of the details of the microscopic sees in his review that all the approaches described by a simple random walk, interactions.’ are disparate. This science is not mature which would lead to a Gaussian distribu­ These days, there are a few teams of yet. Maybe this is a good thing: you don’t tion if you plotted a graph of deviations physicists around the world that have want to unify, you don’t want to make from the norm. In physical systems fluctu- turned their mathematical expertise to everyone agree with one authority.’ ations are usually Gaussian. But in eco­ matters of finance. At the moment econophysicists around nomics, things are different. One of the main tools is the computer the world are trading ideas, speculating ‘In economics, and in these distribu­ model: a simulation of the transactions on the best models and the best strategies tions which Levy discovered, the fluctua­ made by a large group of traders. In for understanding. All are hoping to get tions can be arbitrarily large,’ Solomon Zhang’s model (see page 4) traders can rich with knowledge. (TC) explains.‘And this is very hot stuff; each learn from each other, and trade only one Part 2 next issue: time you see a big fluctuation in the stock stock by assessing past prices. Other An article by Yi-Cheng Zhang 1998 January/February News Europhysics.