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.

中文翻译：

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现货波动率估计器的 Edgeworth 修正

摘要 我们在允许漂移和杠杆效应的对数价格过程的一般假设下，为现货波动率估计器开发了 Edgeworth 扩展理论。该结果基于对偏度和峰度的进一步估计，与现有的二阶渐近正态性结果进行比较。因此，我们的理论可以为现货波动率的有限样本分布提供细化结果。我们还通过使用 Edgeworth 展开来构建现货波动率的可行置信区间（一侧和两侧）。我们进行的蒙特卡罗模拟研究表明，基于 Edgeworth 展开的区间比基于正态近似的常规区间表现更好，这证明了我们理论结论的正确性。