Volatility Clustering: A Nonlinear Theoretical Approach

Abstract

This paper verifies the endogenous mechanism and economic intuition on volatility clustering using the coexistence of two locally stable attractors proposed by Gaunersdorfer, Hommes and Wagener (2008). By considering a simple asset pricing model with two types of boundedly rational traders, fundamentalists and trend followers, and noise traders, we provide conditions on the coexistence of locally stable steady state and invariant cycle of the underlying nonlinear deterministic financial market model and show numerically that the interaction of the coexistence of the deterministic dynamics and noise processes can endogenously generate volatility clustering and long range dependence in volatility observed in financial markets. Economically, volatility clustering occurs when neither the fundamental nor trend following traders dominate the market and when traders switch more often between the two strategies.

Keywords: Volatility clustering, fundamentalists and trend followers, bounded rationality, stability, coexisting attractors.

JEL Classification: D84, E32, G12