A simple microstructure return model explaining microstructure noise and Epps effects

TL;DR

This paper introduces a simple microstructure return model that explains key phenomena like microstructure noise and Epps effects by combining ARFIMA processes, bid-ask bounce, fat tails, and non-Poissonian trade intervals, matching observed stylized facts.

Contribution

The model provides a unified explanation for microstructure noise and Epps effects, integrating multiple known market microstructure features into a coherent framework.

Findings

The model reproduces short-range return correlations.

It explains long-range absolute return correlations.

It accounts for the microstructure noise and Epps effects quantitatively.

Abstract

We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of microstructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time scale used to estimate it. Paradoxically, the Epps effect states that cross correlations between asset returns are increasing functions of the time scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time scale in the presence of the long memory process (i).