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

TL;DR

This paper introduces a modified Mike-Farmer model incorporating long memory in order aggressiveness, successfully reproducing long memory in volatility while maintaining other market stylized facts.

Contribution

The paper proposes a novel modification to the Mike-Farmer model by adding long memory in order aggressiveness, capturing long memory in volatility observed in real markets.

Findings

Long memory appears in volatility with a DFA exponent of about 0.76.

The cubic law of returns and diffusive price behavior are preserved.

Long memory of order signs does not affect volatility long memory.

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.