Asset-specific limit order microstructure noise: Parameter estimation and empirical evidence

Abstract

The one-sided microstructure noise model for high-frequency quotes from a limit order book is generalized to capture asset-specific noise tail behaviour. Estimation of a noise tail parameter becomes the key step for inference. This is possible based on moments of the high-frequency returns when specifying a parametric noise model. For a Gamma noise distribution, we establish a central limit theorem for 1-dependent observations from the resulting Gamma difference distribution and prove that it is valid also in the convolution model with general semimartingale log-price dynamics. We highlight that the noise tail parameter has important implications for estimating the efficient price and its volatility. An empirical analysis of recent NASDAQ limit order book data demonstrates that asset-specific noise tail parameters are relevant in practice.