Local mispricing and microstructural noise: A parametric perspective

We extend the classic ”martingale-plus-noise” model for high-frequency returns to accommodate an error correction mechanism and endogenous pricing errors. It is motivated by (i) novel empirical evidence documenting that microstructure noise exhibits frequently changing patterns of serial dependence which are interwoven with innovations to the efficient price; (ii) building a bridge between high-frequency econometrics and market microstructure models. We identify temporal pricing error correction and noise endogeneity as complementary components driving high-frequency dynamics and inducing two separate regimes, characterized by the sign of the return serial correlation and an implied bias in realized variance estimates. We document frequent fluctuations between these regimes, which can be associated with price discovery in a setting with incomplete information and learning. The model links critical concepts from high-frequency statistics and market microstructure theory, suggesting new avenues for volatility estimation.