Jump Robust Volatility Estimation and Jump Tests using Renewal Processes

Trading in stocks and other financial instruments nowadays predominately takes place on electronic
trading platforms using limit order books. Every trading event is recorded with (at least) millisecond
time-stamps, which generates large high-frequency datasets with very clean information about the
trading process. Statistically the time-stamps in such a series of trading events are described best as
a point process, because events are irregularly spaced in time.
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My 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 jump
test statistics and inference procedures and 3) apply these tests to assess jump risk premia, that
investors require as compensation to hold very "jumpy" assets. The volatility estimators and tests that
will be developed during my PhD have the potential to outperform the latest existing statistics and
tests in the Realized Volatility (RV) literature, as our methodology will allow to exploit the richest
possible information set from both empirical and theoretical points of view. RV estimators are
typically only constructed from sparse (in many cases artificially obtained) equidistant information
sets, while our methodology will allow us to exploit every single event and therefore the complete
trading history and complete price path. This is of utmost importance for the precise identification of
price jumps and volatility bursts.
My PhD research will advance the existing literature on deriving and forecasting volatility estimators
and more general risk measures using high-frequency data. Traditionally high-frequency data has
been shown to be highly beneficial for this purpose through the use of RV estimators. Initially
proposed by Anderson, Bollerslev, Diebold and Labys (1999), the RV estimator is a non-parametric
volatility measure, constructed by summing up intraday squared returns. The introduction of RV
estimators aims to estimate the quadratic variation (QV) or the integrated variance (IV) of a price
series over some interval of time in order to measure the ex-post variation of asset prices. This
approach, however, requires us to overcome some challenges.
We often observe jumps in asset price and/or volatility series. As noted by Andersen, Bollerslev and
Diebold (2007), Barndorff-Nielsen and Shephard (2006), most of the "rare'' large jumps are usually
related to arrival of unexpected information, such as macroeconomic news announcements. Small
jumps become more and more apparent the more we "zoom-in'' into the high-frequency data and
are 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 they
represent a significant source of non-diversified risk. So, testing for jumps in asset price and/or
volatility series and treating jumps appropriately in volatility modelling is meaningful for financial
market participants as they normally want to be compensated by a risk premium for holding a
"jumpy" asset