In An Introduction to Econophysics, Rosario N. Mantegna and H. Eugene Stanley seek to discuss the application to financial markets "of such concepts as power-law distributions, correlations, scaling, unpredictable time series, and random processes." These are concepts that have had considerable impact on the physical sciences. The implicit suggestion is that there is a field called "econophysics," which is the application of mathematical techniques to the modeling and analysis of financial markets and economic systems. The book is an overview and introduction to the field by two respected physicists--Mantegna, of Palermo University in Italy and Stanley, of Boston University--presumably written for physics or mathematics professionals with limited knowledge of finance.

How should we judge An Introduction to Econophysics as a book and econophysics as a field? A quick glance at the bibliography reveals a large volume of work devoted to the field, generally culled from physics journals, a few finance journals, and a number of basic books on physics. A single page of the bibliography contains titles as diverse as "Turbulence and Financial Markets" (published by the authors in Nature, "Dynamical Optimization Theory of a Diversified Portfolio" published in Physica A, and Mandan Mehta's Random Matrices (Academic, 1990). The evidence suggests a lot of activity in the field, but the question is: Does this mean the field is important? To judge, we have to investigate the aims of modern financial theory and whether econophysics supports these aims.

The aim of modern financial theory (or at least that part of modern finance having to do with financial markets) might be described as an attempt to produce theoretical models describing the behavior of financial markets, with an eye toward causal mechanisms, statistical laws, and even predictive power. Starting with assumptions about the behavior of rational economic agents, one makes restrictions on the set of possible laws describing financial markets. Adding simplifying assumptions such as frictionless markets, an absence of transaction costs, and unlimited short selling, the analysis is brought into the realm of the tractable. By observing the behavior of actual financial markets, through the collection and analysis of time series of financial data, one ultimately eliminates many models that are a priori possible but contrary to observed behavior. From these observations theories are refined and advanced, while all along there are opportunities for missteps, debates, and outright bad science. In the process of analysis, tools and methodologies from a number of sciences may be brought to bear on the problem as well.

Unfortunately, An Introduction to Econophysics completely ignores questions of financial theory and a great deal of the vast financial literature on capital markets and option pricing produced over the past 30 years. Moreover, it never attempts to establish the contribution of its methods to the field of finance. Rather, it positions itself as a field that can lend insight to the workings of financial markets. Yet many chapters end with conclusions as fuzzy as that of chapter 11: "Indeed no analog of the 2/3 law appears to hold for price dynamics."

As to the field itself, one would hope that the toolchest of analytic techniques developed for studying physical systems would have application to finance. However, such applications must be measured in terms that are useful to finance itself. An Introduction to Econophysics fails to deliver a cogent argument as to why this is so. Why it might be so is firmly established, but this is not enough.

The book also fails to discuss some fundamental and important differences between physics and finance, such as the inability to produce financial laws that persist over time, as compared to the constancy of physical laws (drop a rock off a tower 400 years ago and the rock obeys the same physical laws as it does today). In the end, the reader is left with the impression that the authors, both capable and accomplished in their fields, are in the midst of creating a new field, one that exists alongside traditional finance while, at the same time, is outside of it. The question remains whether this new field will be interesting to an audience broader than physicists, and in particular whether practitioners of mainstream finance will find useful the tools offered by econophysics.

© 2001 American Institute of Physics