A consensus-based dynamics for market volumes

We develop a model of trading orders based on opinion dynamics. The agents may be thought as the share holders of a major mutual fund rather than as direct traders. The balance between their buy and sell orders determines the size of the fund order (volume) and has an impact on prices and indexes. We assume agents interact simultaneously to each other through a Sznajd-like interaction. Their degree of connection is determined by the probability of changing opinion independently of what their neighbours are doing. We assume that such a probability may change randomly, after each transaction, of an amount proportional to the relative difference between the volatility then measured and a benchmark that we assume to be an exponential moving average of the past volume values. We show how this simple model is compatible with some of the main statistical features observed for the asset volumes in financial markets.