Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise

TL;DR

This paper introduces a new estimator for intraday spot volatility using high-frequency order prices affected by microstructure noise, providing theoretical guarantees and demonstrating good finite-sample performance.

Contribution

It proposes a simple, explicit estimator based on local order statistics for high-frequency data with microstructure noise, along with consistency and asymptotic normality results.

Findings

Estimator is consistent and asymptotically normal.

Finite-sample performance is validated through Monte Carlo simulations.

Efficient numerical algorithm for bias correction is developed.

Abstract

We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an It\^o semimartingale with jumps and general stochastic volatility, we present a simple and explicit estimator using local order statistics. We establish consistency and stable central limit theorems as asymptotic properties. The asymptotic analysis builds upon an expansion of tail probabilities for the order statistics based on a generalized arcsine law. In order to use the involved distribution of local order statistics for a bias correction, an efficient numerical algorithm is developed. We demonstrate the finite-sample performance of the estimation in a Monte Carlo simulation.