Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fact or friction: Jumps at ultra high frequency

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

TL;DR

This paper challenges the conventional view that jumps dominate price variability by leveraging millisecond-tick data and noise-robust pre-averaging to separate diffusion and jump components. It develops $RV^*$ and $BV^*$ estimators and defines $JV^* = RV^* - BV^*$ to measure jump variation, showing that jumps account for roughly 1% of total quadratic variation, far less than lower-frequency studies. The results, consistent across US equities and FX pairs, suggest many previously identified jumps at coarser frequencies are actually bursts of volatility or liquidity shocks rather than discrete price jumps. The findings have implications for pricing, risk management, and hedging, highlighting the critical role of data frequency and market microstructure effects in interpreting high-frequency price dynamics.

Abstract

This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive set of ultra high-frequency equity and foreign exchange tick data recorded at millisecond precision, allowing us to examine the price evolution at the individual order level. We show that in both theory and practice, traditional measures of jump variation based on lower-frequency data tend to spuriously assign a burst of volatility to the jump component. As a result, the true price variation coming from jumps is overstated. Our estimates based on tick data suggest that the jump variation is an order of magnitude smaller than typical estimates found in the existing literature.

Fact or friction: Jumps at ultra high frequency

TL;DR

This paper challenges the conventional view that jumps dominate price variability by leveraging millisecond-tick data and noise-robust pre-averaging to separate diffusion and jump components. It develops and estimators and defines to measure jump variation, showing that jumps account for roughly 1% of total quadratic variation, far less than lower-frequency studies. The results, consistent across US equities and FX pairs, suggest many previously identified jumps at coarser frequencies are actually bursts of volatility or liquidity shocks rather than discrete price jumps. The findings have implications for pricing, risk management, and hedging, highlighting the critical role of data frequency and market microstructure effects in interpreting high-frequency price dynamics.

Abstract

This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive set of ultra high-frequency equity and foreign exchange tick data recorded at millisecond precision, allowing us to examine the price evolution at the individual order level. We show that in both theory and practice, traditional measures of jump variation based on lower-frequency data tend to spuriously assign a burst of volatility to the jump component. As a result, the true price variation coming from jumps is overstated. Our estimates based on tick data suggest that the jump variation is an order of magnitude smaller than typical estimates found in the existing literature.
Paper Structure (16 sections, 1 theorem, 30 equations, 11 figures, 3 tables)

This paper contains 16 sections, 1 theorem, 30 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Jump measurement from noisy tick data
  3. A model for noisy tick data
  4. Measurement of the jump component
  5. Simulation study
  6. The role of the jump component in currency and US equity data
  7. Data description
  8. The magnitude of the jump component
  9. The burst of volatility hypothesis
  10. A burst of volatility simulation
  11. Further empirical results
  12. Concluding remarks
  13. Proofs
  14. The explicit form of $\Sigma^\ast$
  15. Consistency with irregular sampling
  16. ...and 1 more sections

Key Result

Proposition 1

Assume that $Y$ follows Eq. Eqn:Yprocess and that $E(u^4) < \infty$. As $N \to \infty$, it holds that Moreover, suppose that $E(u^8)<\infty$, and that $X$ is a continuous semimartingale, i.e., $X$ follows Eq. Eqn:Xprocess but with $N_t^J \equiv 0$ for all $t$, and with condition (V) as listed in the proof fulfilled. As $N \to \infty$, it then further holds that a mixed normal distribution with c

Figures (11)

  • Figure 1: The S&P 500 flash-crash: Jump or burst in volatility?
  • Figure 2: An illustration of noisy tick data.
  • Figure 3: $\theta$-signature plot of average annualized volatility and jump proportion.
  • Figure 4: Jump proportion, quarter-by-quarter.
  • Figure 5: Regression analysis of bi-power variation against realized variance.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Proposition 1