Staleness Factors and Volatility Estimation at High Frequencies

TL;DR

This paper introduces a model for market price staleness at high frequencies, deriving estimators that correct biases in volatility estimates and demonstrating their practical importance in risk management.

Contribution

It develops a novel maximum likelihood estimation framework for staleness factors, bias correction methods for volatility, and validates these with empirical data.

Findings

Bias in co-volatility estimates due to staleness is significant and correctable.

Bias-corrected estimators are robust and converge at different rates depending on the method.

Staleness factors explain cross-sectional risk premia and improve out-of-sample portfolio risk.

Abstract

In this paper, we propose a price staleness factor model that accounts for pervasive market friction across assets and incorporates relevant covariates. Using large-panel high-frequency data, we derive the maximum likelihood estimators of the regression coefficients, the nonstationary factors, and their loading parameters. These estimators recover the time-varying price staleness probabilities. We develop asymptotic theory in which both the dimension $d$ and the sampling frequency $n$ tend to infinity. Using a local principal component analysis (LPCA) approach, we find that the efficient price co-volatilities (systematic and idiosyncratic) are biased downward due to the presence of staleness. We provide bias-corrected estimators for both the spot and integrated systematic and idiosyncratic co-volatilities, and prove that these estimators are robust to data staleness. Interestingly, besides their dependence on the dimensionality $d$, the integrated plug-in estimates converge at a rate of $n^{-1/2}$ without requiring correcting term, whereas the local PCA estimates converge at a slower rate of $n^{-1/4}$. This validates the aggregation efficiency achieved through nonlinear, nonstationary factor analysis via maximum likelihood estimation. Numerical experiments justify our theoretical findings. Empirically, we demonstrate that the staleness factor provides unique explanatory power for cross-sectional risk premia, and that the staleness correction reduces out-of-sample portfolio risk.