论文标题
与依赖的市场微观结构噪声相比，在无限变化下估计斑点波动率
Estimating spot volatility under infinite variation jumps with dependent market microstructure noise
论文作者
论文摘要
跳跃和市场微观结构噪声是高频财务数据的风格化功能。众所周知，他们在资产的波动率（包括集成和点波动率）中引入了偏见，并且已经提出了许多方法来解决这个问题。当跳跃强烈随着无限变化而大量时，则无法提供串行依赖噪声下斑点波动率的有效估计，因此无需进行。为此，我们提出了一个新颖的斑点波动率，并使用预先计算技术和经验特征功能的混合使用。在轻度的假设下，建立了估计量的一致性和渐近正态性的结果。此外，我们表明，当跳跃具有较低的活动或具有对称结构时，我们的估计器以最佳的差异达到了几乎有效的收敛速率。模拟研究验证了我们的理论结论。我们将提出的估计器应用于经验分析，例如使用第二次交易价格数据估算每周波动率曲线。
Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods have been proposed to deal with this problem. When the jumps are intensive with infinite variation, the efficient estimation of spot volatility under serially dependent noise is not available and is thus in need. For this purpose, we propose a novel estimator of spot volatility with a hybrid use of the pre-averaging technique and the empirical characteristic function. Under mild assumptions, the results of consistency and asymptotic normality of our estimator are established. Furthermore, we show that our estimator achieves an almost efficient convergence rate with optimal variance when the jumps are either less active or active with symmetric structure. Simulation studies verify our theoretical conclusions. We apply our proposed estimator to empirical analyses, such as estimating the weekly volatility curve using second-by-second transaction price data.
