STATISTICAL REVISIT TO THE MIKE-FARMER MODEL: CAN THIS MODEL CAPTURE THE STYLIZED FACTS IN REAL WORLD MARKETS?

Abstract

According to current literature, the Mike-Farmer (MF) model1 is constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully capture the diffusive behavior of stock prices at the transaction level. In our paper, we revisit the statistical properties of the generated series of prices based on the MF model to clarify whether it can reproduce the stylized facts in real world markets. However, the Detrended Fluctuation Analysis (DFA) scaling exponent of volatility Hv ≈ 0.6, which may be slightly lower than that in real markets; while a modified version of the MF model proposed by Gu and Zhou2 can improve the DFA scaling exponent of volatility Hv ≈ 0.75, which is closer to the empirical findings. Finally, we test the existence of another commonly found two stylized facts in the real world: the volatility clustering, and leverage effect.