Time-Variation of Second Moments from a Multi-Agent Noise Trader Model of Speculative Markets

Thomas Lux
Department of Economics, University of Bamberg
Thomas.Lux@sowi.Uni-Bamberg.de

Abstract

This paper considers the dynamics of conditional second moments resulting from a statistical description of agents' attitudes and behaviour in a noise trader/infection framework. The basic aim is to exemplify by means of a simple model how results on the variances of state variables can be obtained in a framework with a heterogeneous ensemble of agents. In general, the dynamics of second moments of state variables (e.g. prices) can be seen to exhibit autoregressive dependence. Furthermore, conforming to well-known empirical findings, volability can change over time, shocks to volatility have lasting effects and mean-reversion in second moments is observed. Thus, this kind of market microstructure modelling can contribute to explain the regularities in variances found in data from asset markets and foreign exchange markets.

Keywords: Noise traders, speculation, market microstructure, heteroscedasticity.