Jump Robust Volatility Estimation and Jump Tests using Renewal Processes

如今，股票和其他金融工具的交易主要是在使用限价订单的电子交易平台上进行的。每个交易事件都有(至少)毫秒时间戳记录，这会产生大量高频数据集，其中包含关于交易过程的非常干净的信息。3我的博士研究项目将利用高频数据集的点过程性质来1)构造跳跃稳健波动率估计器并推导其渐近性质，2)开发跳跃统计和推断程序，以及3)应用这些测试来评估跳跃风险溢价，投资者需要这些溢价作为补偿来持有非常“跳跃”的资产。在我的博士学位期间将开发的波动率估计器和测试有可能超过已实现波动率(RV)文献中最新的现有统计和测试，因为我们的方法将允许从经验和理论角度利用最丰富的信息集。RV估计器通常只能从稀疏的(在许多情况下是人工获得的)等距信息集构建，而我们的方法将允许我们利用每一个单独的事件，从而利用完整的跟踪历史和完整的价格路径。这对于准确识别价格跳跃和波动突发是至关重要的。我的博士研究将推进现有文献，即使用高频数据推导和预测波动率估计器和更一般的风险度量。传统上，高频数据已经被证明是非常有益的，通过使用RV估计器。RV估计器最初由Anderson，Bollerslev，Diebold和Labys(1999)提出，是一种非参数波动率度量，通过求日内平方收益的总和来构造。引入RV估计量的目的是估计价格序列在一段时间内的平方差(QV)或积分方差(IV)，以衡量资产价格的事后变化。然而，这种方法需要我们克服一些挑战。我们经常观察到资产价格和/或波动率序列的跳跃。正如安德森、博勒斯列夫和迪博尔德(2007)、巴恩多夫-尼尔森(Barndorff-Nielsen)和谢泼德(Shephard)(2006)所指出的那样，大多数“罕见”的大幅跳跃通常与意想不到的信息的到来有关，例如宏观经济新闻公告。我们越“放大”高频数据，小幅跳跃就变得越来越明显，部分原因是市场设计特征，如滴答大小和LOB属性。Bollerslev，Law和Tauchen(2008)指出，金融时间序列的跳跃很重要，因为它们代表了非多样化风险的一个重要来源。因此，对资产价格和/或波动率序列的跳跃进行测试，并在波动率建模中适当地处理跳跃，对金融市场参与者来说是有意义的，因为他们通常希望因持有“跳跃”资产而获得风险溢价补偿。

Trading in stocks and other financial instruments nowadays predominately takes place on electronictrading platforms using limit order books. Every trading event is recorded with (at least) millisecondtime-stamps, which generates large high-frequency datasets with very clean information about thetrading process. Statistically the time-stamps in such a series of trading events are described best asa point process, because events are irregularly spaced in time.3My PhD research project will exploit the point process nature of high-frequency datasets to 1)construct jump robust volatility estimators and derive their asymptotic properties, 2) develop jumptest statistics and inference procedures and 3) apply these tests to assess jump risk premia, thatinvestors require as compensation to hold very "jumpy" assets. The volatility estimators and tests thatwill be developed during my PhD have the potential to outperform the latest existing statistics andtests in the Realized Volatility (RV) literature, as our methodology will allow to exploit the richestpossible information set from both empirical and theoretical points of view. RV estimators aretypically only constructed from sparse (in many cases artificially obtained) equidistant informationsets, while our methodology will allow us to exploit every single event and therefore the completetrading history and complete price path. This is of utmost importance for the precise identification ofprice jumps and volatility bursts.My PhD research will advance the existing literature on deriving and forecasting volatility estimatorsand more general risk measures using high-frequency data. Traditionally high-frequency data hasbeen shown to be highly beneficial for this purpose through the use of RV estimators. Initiallyproposed by Anderson, Bollerslev, Diebold and Labys (1999), the RV estimator is a non-parametricvolatility measure, constructed by summing up intraday squared returns. The introduction of RVestimators aims to estimate the quadratic variation (QV) or the integrated variance (IV) of a priceseries over some interval of time in order to measure the ex-post variation of asset prices. Thisapproach, however, requires us to overcome some challenges.We often observe jumps in asset price and/or volatility series. As noted by Andersen, Bollerslev andDiebold (2007), Barndorff-Nielsen and Shephard (2006), most of the "rare'' large jumps are usuallyrelated to arrival of unexpected information, such as macroeconomic news announcements. Smalljumps become more and more apparent the more we "zoom-in'' into the high-frequency data andare partly caused by market design characteristics such as tick size and LOB properties. Bollerslev,Law and Tauchen (2008) note that jumps in a financial time series are important because theyrepresent a significant source of non-diversified risk. So, testing for jumps in asset price and/orvolatility series and treating jumps appropriately in volatility modelling is meaningful for financialmarket participants as they normally want to be compensated by a risk premium for holding a"jumpy" asset