A Return Model for Microstructure Noise and the Epps Effect

Summary

The paper presents a model of tick-level financial returns that combines an ARFIMA process, bid–ask bounce, fat-tailed returns, and non-Poisson trade intervals. It uses these ingredients to explain several observed features of market data: brief correlations in returns, longer-lasting correlations in absolute returns, microstructure noise, and the Epps effect.

In the model, bid–ask bounce creates negative return correlations that help explain why volatility estimates fall as the measurement interval grows. The Epps effect—the increase in measured cross-asset correlation at longer intervals—is attributed to the statistical overlap of return momentum when assets have genuine correlation and returns exhibit long memory. The account is presented as a qualitative and quantitative explanation, but the provided text gives no dataset, parameter estimates, or comparison with alternative explanations, so it does not establish how well the model applies across markets.

Key ideas

• The model combines long-memory returns, bid–ask bounce, fat tails, and non-Poisson trade timing.
• Bid–ask bounce introduces negative short-horizon return correlations.
• Measured volatility can decline as the return-estimation interval increases.
• Measured cross-asset correlations can rise with the interval, producing the Epps effect.
• Long-memory momentum overlap is proposed as an explanation for the Epps effect when assets are genuinely correlated.

Tags

# A simple microstructure return model explaining microstructure noise and Epps effects


# A simple microstructure return model explaining microstructure noise and Epps effects









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).

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