Issue
EPL
Volume 86, Number 4, May 2009
Article Number 48002
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/86/48002
Published online 26 May 2009
EPL, 86 (2009) 48002
DOI: 10.1209/0295-5075/86/48002

Emergence of long memory in stock volatility from a modified Mike-Farmer model

Gao-Feng Gu1, 2, 3 and Wei-Xing Zhou1, 2, 3, 4, 5

1   School of Business, East China University of Science and Technology - Shanghai 200237, China
2   School of Science, East China University of Science and Technology - Shanghai 200237, China
3   Research Center for Econophysics, East China University of Science and Technology - Shanghai 200237, China
4   Research Center on Fictitious Economics & Data Science, Chinese Academy of Sciences - Beijing 100080, China
5   Engineering Research Center of Process Systems Engineering (Ministry of Education), East China University of Science and Technology - Shanghai 200237, China

wxzhou@ecust.edu.cn

received 30 July 2008; accepted in final form 27 April 2009; published May 2009
published online 26 May 2009

Abstract
The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.

PACS
89.65.Gh - Economics; econophysics, financial markets, business and management.
89.75.Da - Systems obeying scaling laws.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.

© EPLA 2009