Jump Robust Volatility Estimation and Jump Tests using Renewal Processes

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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