The Dynamics of the Linear Random Farmer Model

TL;DR

This paper analyzes the Linear Farmer's Model, demonstrating how Pareto-tailed returns and volatility clustering can emerge even with simple strategies, especially at critical trading points.

Contribution

It introduces a probabilistic approach to agent activity in the Linear Farmer's Model and characterizes the conditions for heavy-tailed returns and volatility clustering.

Findings

Pareto-tailed returns can arise with only value investors.

Heavy tails and volatility clustering occur at the zero Lyapunov point.

A procedure for determining the tail exponent is provided.

Abstract

On the framework of the Linear Farmer's Model, we approach the indeterminacy of agents' behaviour by associating with each agent an unconditional probability for her to be active at each time step. We show that Pareto tailed returns can appear even if value investors are the only strategies on the market and give a procedure for the determination of the tail exponent. Numerical results indicate that the returns' distribution is heavy tailed and volatility is clustered if trading occurs at the zero Lyapunov (critical) point.