How Trade Arrivals Shape High-Frequency Return Distributions

Summary

The paper models high-frequency equity returns by separating price changes per trade from the process governing when trades arrive. For a highly liquid near-month E-mini S&P 500 futures contract, it reports that trade-time returns are approximately Gaussian at very fine intervals after accounting for scheduled news. It then combines Gaussian trade-time returns with a modified Markov-Switching Multifractal Duration model of inter-trade times.

The model attributes the heavy tails and volatility clustering seen in clock-time returns to over-dispersed trade durations, even when individual trade-time returns are Gaussian. The authors also extrapolate the relationship between trading rate and volatility to examine market stress. They suggest that physical distance between Chicago and New York/New Jersey may impose a ceiling on systemic volatility and support stability under exceptionally heavy trading. These findings are tied to the studied contract and model assumptions; the proposed geographic limit is an inference, not a general guarantee about market behavior.

Key ideas

• Separating trade-time returns from trade arrivals helps explain high-frequency return patterns.
• Trade-time returns for the studied futures contract are reported as approximately Gaussian at very fine scales after controlling for scheduled news.
• A multifractal duration model captures the distribution of inter-trade times.
• Over-dispersed trade arrivals can produce heavy tails and volatility clustering in clock-time returns.
• The authors propose that physical distance between major trading centers may constrain systemic volatility.

Tags

# The Random Walk of High Frequency Trading


# The Random Walk of High Frequency Trading









This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of high-frequency asset returns both in ordinary clock time and in trade time. We show that when controlling for pre-scheduled market news events, trade-time returns of the highly liquid near-month E-mini S&P 500 futures contract are well characterized by a Gaussian distribution at very fine time scales. Second, we develop a structured and parsimonious model of clock-time returns by subordinating a trade-time Gaussian distribution with a trade arrival process that is associated with a modified Markov-Switching Multifractal Duration (MSMD) model. This model provides an excellent characterization of high-frequency inter-trade durations. Over-dispersion in this distribution of inter-trade durations leads to leptokurtosis and volatility clustering in clock-time returns, even when trade-time returns are Gaussian. Finally, we use our model to extrapolate the empirical relationship between trade rate and volatility in an effort to understand conditions of market failure. Our model suggests that the 1,200 km physical separation of financial markets in Chicago and New York/New Jersey provides a natural ceiling on systemic volatility and may contribute to market stability during periods of extremely heavy trading.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.