Edgeworth corrections for spot volatility estimator

TL;DR

This paper introduces Edgeworth expansion techniques to refine the finite sample distribution of spot volatility estimators, accounting for skewness and kurtosis, and improves confidence interval accuracy.

Contribution

It develops a new Edgeworth expansion framework for spot volatility estimators that incorporates higher moments, enhancing finite sample inference accuracy.

Findings

Edgeworth-based intervals outperform normal approximation intervals in simulations.

The theory accounts for drift and leverage effects in the log-price process.

Feasible confidence intervals are constructed with improved coverage properties.

Abstract

We develop Edgeworth expansion theory for spot volatility estimator under general assumptions on the log-price process that allow for drift and leverage effect. The result is based on further estimation of skewness and kurtosis, when compared with existing second order asymptotic normality result. Thus our theory can provide with a refinement result for the finite sample distribution of spot volatility. We also construct feasible confidence intervals (one-sided and two-sided) for spot volatility by using Edgeworth expansion. The Monte Carlo simulation study we conduct shows that the intervals based on Edgeworth expansion perform better than the conventional intervals based on normal approximation, which justifies the correctness of our theoretical conclusion.