Introduction

Randomness stems from our incomplete knowledge of reality, from the lack of information which forbids a perfect prediction of the future. Randomness arises from complexity, from the fact that causes are diverse, that tiny perturbations may result in large effects. For over a century now, Science has abandoned Laplace's deterministic vision, and has fully accepted the task of deciphering randomness and inventing adequate tools for its description. The surprise is that, after all, randomness has many facets and that there are many levels to uncertainty, but, above all, that a new form of predictability appears, which is no longer deterministic but statistical.

Financial markets offer an ideal testing ground for these statistical ideas. The fact that a large number of participants, with divergent anticipations and conflicting interests, are simultaneously present in these markets, leads to unpredictable behaviour. Moreover, financial markets are (sometimes strongly) affected by external news – which are, both in date and in nature, to a large degree unexpected. The statistical approach consists in drawing from past observations some information on the frequency of possible price changes. If one then assumes that these frequencies reflect some intimate mechanism of the markets themselves, then one may hope that these frequencies will remain stable in the course of time.