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# Stock Market: Rare Events, A French Physicist in Finance

As a child I was fascinated by statistics! I kept records of the performance of football clubs over the years and collected economic indicators such as countries' GNPs and cocoa production. And so when I grew up to become a theoretical physicist, it was not surprising that I chose to work in statistical physics!

The variety of physical situations described by statistical physics and the power of the methods developed and used over the past 50 years make the field particularly exciting. Specializing in this area, one learns how to cope with disorder and noise and how to develop an intuition based on randomness. One of my main research interests is extreme events, and particularly situations where these rare, large events completely dominate the observed phenomena. One example is the so-called "Levy flight," which is a random walk with steps of varying sizes. Usual random walks are made up of steps that are all of similar sizes. Levy flights make tiny steps most of the time but sometimes take gigantic jumps, such that on any time scale, most of the distance has been traveled in just one hop.

In 1990, when I was at the Ecole Normale Supérieure (Paris), I contributed to the interpretation of Levy flight dynamics. This work was published in a paper in La Recherche, which was read by someone working in a bank. He called me to say that this type of intermittent phenomena (often small, sometimes large) was characteristic of financial markets, where big jumps are market crashes. He was interested in extending the Black-Scholes model, a common tool used by financial experts to price a type of derivative called options, by using Levy statistics. He gave me several papers to read, and I have to admit that I felt stranded at first--the mathematics was hard and abstract, even for a theoretical physicist. However, working with a colleague, Didier Sornette, we made a breakthrough which allowed us to produce a new financial model. This system meant that historical data could be used to give a better pricing theory and therefore a possibility of arbitrage on option markets. Furthermore, a better understanding of the theory could help in better risk management.

At that time, I met Jean-Pierre Aguilar, who had founded a financial software company (ATSM) and an automated trading company (CFM). He was very interested in my ideas and thought that a research arm could be very useful to both his companies. This was the birth of Science & Finance, in 1994. We struggled quite a bit getting people interested in what we were doing. Our background, as physicists, did not fit with the more mathematically inclined people we were trying to convince, especially in France. It would have been better in the United States, where the flow of physics Ph.D.s into Wall Street has been going on for some time.

Our first contracts were internal, with ATSM and CFM. We developed a new type of risk-management software, based on these extreme risks ideas (Profiler). We continued publishing scientific papers, wrote a book on financial risks with Marc Potters (the first Science & Finance member), and looked for other applications of ideas from physics in finance: like the idea of modeling the interest rate curve as an elastic string; or the application of the so-called "random matrix theory" to correlation matrices.

Science & Finance has grown at the rate of one new person a year--we now have five full-time researchers, all with Ph.D.s in statistical physics. Our aim is to combine good science and good business. We are convinced that both have to go together: Good science gives the credibility we need in a world where unscientific claims are not rare; good business allows us to fund exciting intellectual ideas. We have now completely renewed the trading engine of CFM and have an exclusive contract with one of the world's largest banks to put together an automated option trading system based on our original ideas on how to go beyond Black-Scholes. We strongly believe that finance is becoming an experimental science, where physicists will play an increasingly larger role and where Science & Finance will, hopefully, have trumps to play.

For more information, scientific papers, and realizations see: http://www.science-finance.fr and the sister sites http://www.cfm.fr and http://www.atsm.fr

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