The drift burst hypothesis

TL;DR

The paper introduces the drift burst hypothesis, embedding an exploding drift into Itô semimartingale price dynamics and developing a nonparametric, high-frequency test to detect drift bursts in real-time data.It shows that drift bursts are theoretically detectable only when drift and volatility bursts satisfy a threshold condition ($\alpha-\beta>\tfrac{1}{2}$) and that volatility bursts are necessary to avoid arbitrage, with robustness to jumps and market microstructure noise.Empirically, drift bursts occur across equities, fixed income, currencies, and commodities at roughly weekly frequencies, and most bursts revert, with larger reversals tied to higher pre-burst volume, consistent with liquidity-provider theories of market microstructure.Overall, the work links drift explosions to flash crashes in a principled framework and provides a practical detection method with implications for understanding liquidity provision and market stability.

Abstract

The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such dynamics, but we argue that drift bursts of varying magnitude are an expected and regular occurrence in financial markets that can arise through established mechanisms of liquidity provision. We show how to build drift bursts into the continuous-time Itô semimartingale model, elaborate on the conditions required for the process to remain arbitrage-free, and propose a nonparametric test statistic that identifies drift bursts from noisy high-frequency data. We apply the test and demonstrate that drift bursts are a stylized fact of the price dynamics across equities, fixed income, currencies and commodities. Drift bursts occur once a week on average, and the majority of them are accompanied by subsequent price reversion and can thus be regarded as "flash crashes." The reversal is found to be stronger for negative drift bursts with large trading volume, which is consistent with endogenous demand for immediacy during market crashes.

Figures (10)

• Figure 1: The U.S. S&P500 equity index and treasury market flash crash.
• Figure 2: Illustration of a log-price with a drift burst.
• Figure 3: Q--Q plot of $\mkern 1.5mu\overline{\mkern-1.5muT\mkern-1.5mu}\mkern 1.5mu_{t}^{n}$ without drift burst.
• Figure 4: Time series of drift bursts.
• Figure 5: Drift burst examples.

Theorems & Definitions (12)

• Theorem 1
• Theorem 2
• Remark 1
• Theorem 3
• Theorem 4
• Theorem 5
• Theorem 6
• Remark 2
• Remark 3
• Lemma 1