Flows of information have changed: Do financial markets remain efficient ?

Abstract

This paper develops a dynamic model of a financial market, using some properties of the formalism of quantum physics. The model aims to take into account several aspects of modern financial markets: Trades take place sequentially and prices change very often in a never ending movement; The state of the market evolves incessantly, the stream of financial information is renewed permanently, and each agent influences the price when he sends an order that is aggregated in a central order book (reciprocally the state of the market influences the decisions of agents). We consider that information is fully and freely available. An essential feature of the model is that information is partitioned in two subsets: Information is effective when it can be processed by an algorithm; If it cannot be processed by an algorithm, it is non-effective. We study the conditions on the nature and the structure of information that make it possible for the market to be efficient or at least powerful. A market is efficient (precisely semi-strong efficient) when the non effective information is negligible compared to effective information. A market is a powerful tool when it integrates information better than any independent agent deciding separately; we call that power the computational strength of the market. We also show that even without semi-strong efficiency, during a bubble, there is a period when the market can keep its computational strength.