An extended Speculation Game for the recovery of Hurst exponent of financial time series

TL;DR

This paper extends an agent-based speculation game model to better recover the Hurst exponent of financial time series by incorporating additional effects beyond pure speculation.

Contribution

The paper introduces a perturbative extension to the speculation game model to improve its ability to replicate the Hurst exponent observed in real financial data.

Findings

Successfully reproduces stylized facts of financial data

Addresses anti-persistence in the original model

Improves Hurst exponent estimation accuracy

Abstract

The speculation game is an agent-based toy model to investigate the dynamics of the financial market. Our model has achieved the reproduction of 10 of the well-known stylized facts for financial time series. However, there is also a divergence from the behavior of real market. The market price of the model tends to be anti-persistent to the initial price, resulting in the quite small value of Hurst exponent of price change. To overcome this problem, we extend the speculation game by introducing a perturbative part to the price change with the consideration of other effects besides pure speculative behaviors.