论文标题
Lévy过程的有效波动率估计，无界变化的跳跃
Efficient Volatility Estimation for Lévy Processes with Jumps of Unbounded Variation
论文作者
论文摘要
基于高频观察的随机过程的统计推断已经是一个活跃的研究领域，已有十多年了。最著名和最广泛研究的问题之一是估计ItôSemimartingale连续成分的二次变化，并跳跃。当跳跃成分有界限时，在文献中提出了几种速率和方差估计器。但是，迄今为止，很少有方法可以处理无界变化的跳跃。通过开发Lévy过程截断时刻的新高阶扩展，我们为一类无限变化的Lévy过程构建了一个新的速率和差异估计器，其小跳跃的表现就像是稳定的Lévy流程，其稳定的lévy流程与Blumenthal-Getoor Index的稳定流程相比，小于8/5美元。所提出的方法是基于对该过程的截短二次变异的两步偏差程序。我们的蒙特卡洛实验表明，该方法在我们的理论框架所涵盖的环境中的文献中优于文献中的其他有效替代方案。
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic variation of the continuous component of an Itô semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed in the literature when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of the truncated moments of a Lévy process, we construct a new rate- and variance-efficient estimator for a class of Lévy processes of unbounded variation, whose small jumps behave like those of a stable Lévy process with Blumenthal-Getoor index less than $8/5$. The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.
