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.

翻译：本文研究具有单侧微观结构噪声的随机边界模型中高频限价订单价格的现货波动率估计问题。基于含跳跃和一般随机波动的Itô半鞅的离散含噪观测值，我们利用局部次序统计量提出一种简洁显式的估计量。我们建立了相合性和稳定中心极限定理作为渐近性质。该渐近分析基于广义反正弦定律对次序统计量尾部概率的展开。为利用涉及局部次序统计量分布进行偏差校正，开发了一种高效数值算法。我们通过蒙特卡洛模拟验证了该估计量的有限样本性能。