Shared information in the stock market

In this paper we exploit the principle of maximum entropy to gain insight into the process underlying the internal dynamics of a stock market. We first introduce a simplified physical model, the ideally liquid stock, to describe market price evolution and derive an operational definition of price volatility in non-stationary conditions. Using this model we perform an analysis of the information entropy which we compare with market data of stocks traded on the Italian stock exchange in Milan. This leads us to identify constraints to a procedure of entropy maximization and to describe the bulk of the volatility distribution on very general grounds. The nature of the two constraints we find is discussed and related to information available to all market participants. Finally, a stochastic process able to reproduce these findings is presented and the origin of the two constraints is clarified.