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电子交易平台上使用限价订单簿进行的。每一个交易事件都被记录了（至少）毫秒的时间戳，这会产生大量的高频数据集，其中包含关于交易过程的非常清晰的信息。从统计学上讲，这样一系列交易事件中的时间戳最好阿萨点过程来描述，因为事件在时间上是不规则间隔的。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）构建跳跃稳健波动率估计并推导其渐近性质，2）开发跳跃检验统计和推理程序，3）应用这些检验来评估跳跃风险溢价，投资者要求作为补偿持有非常“跳动”的资产。在我的博士学位期间开发的波动率估计和测试有可能超越最新的已实现波动率（RV）文献中的现有统计和测试，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估计量通常仅由稀疏（在许多情况下是人工获得的）等距信息集，而我们的方法将使我们能够利用每一个单一的事件，因此完整的交易历史和完整的价格路径。这是最重要的精确识别价格跳跃和波动爆发。我的博士研究将推进现有的文献推导和预测波动估计和更一般的风险使用高频数据进行测量。传统上，高频数据已被证明是非常有益的，通过使用RV估计。RV估计是由安德森、Bollerslev、Diebold和Labys（1999）首先提出的一种非参数波动性度量方法，它是通过对日内收益率的平方求和来构造的。RVestimators的引入旨在估计价格序列在一定时间间隔内的二次方差（QV）或综合方差（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Andersen，Bollerslev and Diebold（2007），Barndorff-Nielsen and Shephard（2006）所指出的，大多数“罕见”的大幅跳跃通常与意外信息的到来有关，例如宏观经济新闻公告。小跳跃变得越来越明显，我们越“放大”到高频数据，部分是由市场设计特征，如最小报价和LOB属性。Bollerslev，Law和Tauchen（2008）指出，金融时间序列中的跳跃很重要，因为它们代表了非多样化风险的重要来源。因此，检验资产价格和/或波动率序列中的跳跃并在波动率建模中适当处理跳跃对金融市场参与者来说是有意义的，因为他们通常希望通过持有“跳跃”资产的风险溢价得到补偿

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