Book review by F. Cuypers

appeared in Physics Today, March 2004

Why Stock Markets Crash
Didier Sornette

"The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious... The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift." This is how in his recent book Didier Sornette quotes Eugen Wigner. And this may also well be the very message of the book.

Sornette is both a statistical physicist and a member of a new breed of scientist: the econophysicist. Econophysics brings together the worlds of physics, economics and finance to analyze how, collectively, society behaves. But this is not just a book about finance and economics. It is also a mesmerizing introduction to game theory, fractals, catastrophe theory, critical phenomena and much more.

No prior knowledge of finance or economics is needed to understand the book. On the other hand, readers unfamiliar with critical phenomena may become inspired to learn more about this discipline, and experts in the field may enjoy seeing them applied in an unfamiliar context. Throughout the book, Sornette also makes numerous vivid comparisons with many other fields where the many mathematical tools he describes can be applied. Although it seems in places that he is trying to accommodate too-wide-a readership, for the most part, the book successfully bridges the often wide gaps between fields and skills.

The first chapters provide a thought-provoking introduction to finance theory, with a clear description of its failure to explain extreme events. These pages require no familiarity with the subject matter because Sornette sticks to the essentials. However, in doing so he presents them in such an original light, making these chapters enjoyable even for the experienced reader.

Sornette then describes extreme events as phase transitions, and illustrates how the path to criticality is paved. In doing this, he leads us into a fascinating journey through geology, psychology, biology, paleozoology: all related to finance and economics by critical phenomena. In many places a curious reader may wish a topic to be treated in greater depth. But then Sornette never intended to write an encyclopedia and, in any case, he provides an abundant bibliography from standard journals.

The book goes on to verify Sornette's theory against historic financial data. These penultimate chapters are sadly dull in comparison with the earlier parts of the book. Sornette accumulates dreary time series plots with opaque fits, and his text is plagued with inconsistent notations and mind numbing displays of tables filled with irrelevant data - all too suggestive of rehashing previous papers to meet the publisher's deadline. One more focused chapter instead of three may have better carried the message across. Most physicists are loath to cast the first stone, but the general audience may well resent the break of the spell.

In his final chapter, Sornette widens the scope of his analysis to include global economic data. He observes the onset of a phase transition and predicts that around 2050 the world economy is likely to shift into another regime. The evidence is as (un)convincing as in the previous chapters, but the prediction is precise and bold.

Reaching the end of the book one may feel confronted with ambivalent impressions. On the one hand, the unsatisfactory and correct feeling that this is still work in progress, and on the other hand the gratifying prospects of still lots to discover. At this stage, Sornette provides many clues as to why stock markets crash. However, the many references to the renormalization group, network theory and complex fractal dimensions still appear as anecdotal analogies.

Most physicists are unlikely to feel impressed by the quality of the fits to the data. The models seem to contain many parameters and little is said about the goodness of the fits. Sornette insists on the universality of the values taken by some of the parameters - such as critical exponent and scaling ratio - but offers little evidence for this phenomenon, nor any kind of physical interpretation. In essence, the evidence is intriguing but not yet too convincing.

In summary, whilst the book may contain a couple of weaker chapters, it nevertheless provides a captivating account of recent developments in econophysics. I thoroughly enjoyed the reading and substantially widened my horizons in the process. Perhaps the book may inspire more physicists to also extend the scope of their investigations to new realms and maybe, like Sornette, to become founding members of new branches of physics.

Frank Cuypers is Head of Intellectual Property and member of the Executive Team at Swiss Re. He was previously chief actuary at Zurich Re, developing its risk and capital allocation methodology. He became an actuary after working for 13 years in theoretical physics.