Statistical Inference for High Frequency Data

该项目将研究隐藏半鞅模型背景下波动类对象的估计。除波动性外，我们还关注协变、方差分析、杠杆效应和相关数量。该项目使用邻近和无偏估计的思想来找到这样的估计量。假设数据具有高频率，因此将使用小间隔渐近。项目的一个主要部分与这些估算器的应用有关。研究者在非参数、基于交易的期权风险管理方面的早期发现将与估计器相结合，以找到安全解除危险头寸的完整程序。估计器还将与预测技术相结合，为潜在波动率模型（如GARCH）提供基于高频的竞争对手。在这里我们可以利用高频估计中的鞅型误差结构。评估者在项目组合管理方面的经济价值也将被研究。该项目的主要背景是越来越多的金融证券价格高频数据的可用性。原则上，这允许非常精确地确定波动性和类似的价格特征。然而，调查人员发现，价格表现得好像存在测量误差，这引发了一系列关于统计数据如何执行的问题。这个项目将涉及评估，以及对风险管理、预测、投资组合管理和法规的应用。投资者、监管机构和政策制定者都对研究结果感兴趣。

The project will investigate the estimation of volatility-like objects in the context of the hidden semi-martingale model. Apart from volatility, we are concerned with co-variations, ANOVA, leverage effect, and related quantities. The project uses ideas from contiguity and unbiased estimation to find such estimators. Data are assumed to have high frequency, so that small-interval asymptotics will be used. A main part of the project is concerned with the applications of such estimators. The investigator's earlier findings on nonparametric, trading based, risk management for options will be interfaced with the estimators to find complete procedures for safely unwinding dangerous positions. The estimators will also be combined with forecasting techniques to provide high-frequency based competitors to latent volatility models like GARCH. We can here draw on the martingale type error structure in the high frequency estimation. The economic value of the estimators in terms of portfolio management will also be investigated. A main background for the project is the increasing availability of high frequency data for financial securities prices. This permits, in principle, very precise determination of volatility and similar characteristics of prices. The investigator's finding, however, that prices behave as if they have measurement error, raises a number of questions about how the statistics is carried out. This project will be concerned with both estimation, and applications to risk management, forecasting, portfolio management, and regulation. The results are of interest to investors, regulators, and policymakers.