Fact or friction: jumps at ultra high frequency

By Kim Christensen, Roel C. A. Oomen, Mark Podolskij. 2014

198 citations recorded by the source corpus.

In this paper, we demonstrate that jumps in financial asset prices are not nearly as common as generally thought, and that they account for only a very small proportion of total return variation. We base our investigation on an extensive set of ultra high-frequency equity and foreign exchange rate data recorded at milli-second precision, allowing us to view the price evolution at a microscopic level. We show that both in theory and practice, traditional measures of jump variation based on low-frequency tick data tend to spuriously attribute a burst of volatility to the jump component thereby severely overstating the true variation coming from jumps. Indeed, our estimates based on tick data suggest that the jump variation is an order of magnitude smaller. This finding has a number of important implications for asset pricing and risk management and we illustrate this with a delta hedging example of an option trader that is short gamma. Our econometric analysis is build around a pre-averaging theory that allows us to work at the highest available frequency, where the data are polluted bymicrostructure noise. We extend the theory in a number of directions important for jump estimation and testing. This also reveals that pre-averaging has a built-in robustness property to outliers in high-frequency data, and allows us to show that some of the few remaining jumps at tick frequency are in fact induced by data-cleaning routines aimed at removing the outliers.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b18c786349d8d68d6fedd42e6a1ffa388b255b95

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Citations in the corpus

The drift burst hypothesis (2016, unknown): “This relates to a puzzle put forward by Christensen, Oomen, and Podolskij (2014), who find that the total return variation that be attributed to the discontinuous jump component is an order of magnitude smaller than had previously been reported by extensive empirical literature on the topic.”
Decoupling the Short- and Long-Term Behavior of Stochastic Volatility (2016, methodology): “Sufficient, but not necessary, conditions for this are, e.g., that the jump term is given by a compound Poisson process and the noise term is iid with zero-mean and finite fourth moment, and independent of the efficient price Y (Christensen et al., 2014, Proposition 1).”
Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence (2014, background): “Moreover, Christensen, Oomen, and Podolskij (2014) showed that, when considering data sampled at the tick-by-tick level, jumps are detected far less frequently than based on a coarser sampling grid.”
Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “Note also that recent empirical research by Christensen et al. (2011) based on ultra high frequent asset price data suggests that rapid price movements might be often caused by rapid movements in the volatility rather than by price jumps.”
High-Frequency Jump Analysis of the Bitcoin Market* (2017, background): “nd (2008) develop statistical tools to test for the presence of jumps. Their modeling approach assumes that the data is not contaminated by microstructure noise, preventing a high-frequency analysis. Christensen et al. (2014) show that it is crucial to test for jumps at a high frequency to avoid mis”
Systemic Co-Jumps (2017, unknown): “If the discontinuity is in the fundamental price, due to big news, it then materializes in the form of an apparently continuous movement of the traded price, explaining the findings of Christensen et al. (2014).”
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment (2017, unknown): “…and Schaumburg (2012); Dette, Golosnoy, and Kellermann (2016) diurnal effects inject a strong Jensen’s inequality-type bias in some of these estimators; an effect that is reinforced and magnified with a high “volatility-of-stochastic volatility” (e.g., Christensen, Oomen, and Podolskij, 2014).”
Understanding Systematic Risk: A High‐Frequency Approach (2020, unknown): “Christensen, Oomen, and Podolskij (2014) use ultra high-frequency data and estimate that the jump variation accounts for about 1% of total variation.”