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

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 inverse cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatilities in the MF model do 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 a new stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatilities synthesized from the modified MF model with a Hurst exponent close to 0.8, and the inverse 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 of volatilities, while 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