Rough survey of how ticks all add up

Nothing is certain in finance (or physics); true professionals live with this even if theorists cannot. While any text that states that a theorem "ensures" a behaviour of price change is suspect, econophysics interprets market dynamics within a carefully argued theoretical framework. The opening to chapter nine summarises the whole of R. Mantegna and H. E. Stanley's An Introduction to Econophysics : "No model existsI that is accepted by all researchers. In this chapter we present one view."

The view is that financial time series are, to an excellent approximation, scaling and self-similar; both strengths and weaknesses of this view are examined. The authors led the development of this theoretical approach, and the first chapter includes a nice justification for neglecting other approaches, alas without alternative references. Indeed, the major problem with the book is that it is more a survey than an introduction: too much detail without sufficient motivation. Non-essential mathematics is included at the expense of the clear explanation of notions likely to be unfamiliar to the targeted readership, "students and researchers studying economics and physics at the graduate level and professionals in the field of finance".

In practice, the text may prove most useful to physicists interested in this particular approach to finance. Careful reading is required to distinguish what would be observed given a stochastic process from which observations indicate that the underlying process really is stochastic. While technically correct, the jargon is misleading: a "short-range correlated" signal may be predictable in the long range, but a "long-range correlated" signal may not be predictable at all in the gambler's sense.

The text introduces a menagerie of stochastic processes, from random walks to Garch models. There are useful discussions on quantifying relationships between individual stocks and contrasting idealised markets with real markets. The text is supported by many figures interpreting data from finance (and from physics). There are no problem sections or suggested exercises.

Indeed, for a book focused on "empirical analysis methods", there is little or no discussion of technical issues concerning the analysis of real data or quantifying the significance of an calculation. The reader is expected already to distinguish volume from the number of ticks, and a tick (representing an actual trade) from a quote (representing a potential offer). There is no accompanying disk, data or website. An appendix defines notation by chapter (the notation is not consistent throughout). These are definitions rather than explanations. Given the normalisation of jargon required in any transdisciplinary work, a glossary would have been of great value.

The book is naive only in its self-justification: it presents econophysics as a brave new field in which "prior to the 1990s, very few professional physicists did any research". Yet even in the mid-1980s, Columbia University physics students were in demand on Wall Street, and they were being recruited by physicists already there. No doubt finance has funded "rocket scientists" since the first rockets. The difference is not those doing research but the number publishing it; it is these communities along with (other) statistically sophisticated traders who will most benefit from this book.

Leonard A. Smith is reader in statistics, London School of Economics, and fellow of Pembroke College, Oxford.