Fact or Friction: Jumps at Ultra High Frequency

Abstract

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.