Two-Event Models of Order Flow and Market Impact

Summary

This paper compares two linear ways to describe how executed orders affect prices. The Transient Impact Model weights past market-order signs through a propagator, while the History Dependent Impact Model links price changes to the gap between an observed order sign and its expected value, treating that effect as permanent. The authors argue that both should also account for past returns.

They separate price-changing events from events that leave the price unchanged and incorporate both into two-event propagator models. This improves the description of impact, especially for large-tick stocks where price moves are infrequent and informative, and captures excess anti-correlation between earlier returns and later order flow. The reported advantage of the history-dependent models over transient models is modest. The excerpt gives no sample, calibration details, or operational trading results, and its claims concern explanatory fit rather than demonstrated strategy profitability.

Key ideas

• Transient impact models weight past market-order signs using a propagator function.
• History-dependent models connect price changes to deviations of order signs from their expected level.
• Separating price-changing and non-price-changing events improves impact descriptions, especially for large-tick stocks.
• Two-event models capture anti-correlation between past returns and later order flow that one-event models miss.
• The reported fit advantage for history-dependent models is small and does not establish trading profitability.

Tags

# Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact


# Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact









Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. An alternative description -- the History Dependent Impact Model (HDIM) -- assumes that the deviation between the realised order sign and its expected level impacts the price linearly and permanently. The two models, however, should be extended since prices are a priori influenced not only by the past order flow, but also by the past realisation of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. Two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models. Our results document the superior performances of the HDIMs even though only in minor relative terms compared to TIMs. This is somewhat surprising, because HDIMs are well grounded theoretically, while TIMs are, strictly speaking, inconsistent.

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