Evidence for a hyperbolic-like distribution of asset returns drawn from a simple economical financial markets model

Abstract

Risk management and asset pricing benefit from simple functional descriptions of the distribution of real asset returns. Recently, several authors have proposed that asset returns in real stock markets are distributed according to a hyperbolic distribution. While asset returns are generated by trades over time, the natural question is: What does economic theory imply concerning return distributions? We propose a simple model of price formation and, thus, return distribution which is based on economic reasoning. The market’s behavior is represented by a pair consisting of a time-constant strategy and a dynamical trading strategy generating a flow between funds. Simulations of the price dynamics generate returns with fat-tail behavior in line with that of a hyperbolic distribution, and also volatility clustering, which is a mayor stylized fact of asset returns.