Critical Crashes?

In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena. Stochastic dynamics is a commonly used approach to describe the time evolution of financial markets. The large number of agents, their complex mutual influence and obscure decision making all of these leave the probabilistic picture as the only viable way to describe and, as a test, to predict financial markets. In the case of a stable market such a probabilistic description is on solid ground. Indeed, for the stable market the difference between the numbers of “buy” orders and “sell” orders is small and fluctuates around zero which results in corresponding fluctuations of the price of the traded asset. It means that peculiarities of individual decisions are mutually offset, the characteristic fluctuation time is less than the characteristic time of changes of external (fundamental) conditions and number of observations allows meaningful use of statistical procedures such as averaging. However the situation changes dramatically when the overwhelming number of market participants share the same view on the future and make the same orders (for example, order to sell) thus creating a market instability. The participants start to behave “coherently” and to create a realistic picture of such market one needs to model the decision making leading to such behaviour. The modelling of this decision making is the principle problem since the corresponding price movements are simple consequence of the demand-supply mechanism of price fixing. The “coherence” of such events and their extremely low frequency make a statistical description dubious and the whole problem even more challenging. Taking into account the immense importance of crashes as well as “bubbles” for financial systems and the world economy as a whole it is not surprising that the problem of description and prediction of the events attract a lot of efforts and attention. In this note we concentrate on the recently suggested analogy between critical phenomena and the financial crashes. ∗E-mail: [email protected]