Modeling metaorder impact with a Non-Markovian Zero Intelligence model
Modeling metaorder impact with a Non-Markovian Zero Intelligence model
The paper introduces a Non-Markovian Zero Intelligence (NMZI) model for limit order books, specifically designed for small-tick assets. The key innovation is making the probability of limit order signs (buy/sell) depend on an exponentially weighted mid-price return, which captures the reaction of traders with reservation prices to past price trends. This introduces memory into the order flow, breaking the Markovian assumption of the standard Zero Intelligence model. The model is calibrated using Tesla data and shown to reproduce empirically observed concave price impact during metaorder execution and subsequent price reversion, which the standard ZI model fails to capture.
The authors provide both numerical simulations and analytical derivations to explain the mechanisms behind the concave impact. They show that the concavity results from the interplay between the direct impact of child market orders and the indirect impact from changes in limit order arrival rates due to the price-dependent sign probability. The model's behavior is controlled by two parameters: α (reaction strength) and β (memory time scale). The stationary regime during execution yields a linear price path with slope determined by these parameters, while after execution the price decays exponentially. The NMZI model offers a parsimonious, explainable alternative to more complex LOB simulators, with computational efficiency and the ability to replicate key stylized facts of market impact for small-tick assets.
Highlights
- 1Proposes a Non-Markovian Zero Intelligence (NMZI) model for small-tick assets that reproduces concave price impact during metaorder execution and price reversion after execution.
- 2Introduces a time-varying probability for limit order signs based on exponentially weighted mid-price return, capturing trader reaction to price trends.
- 3Provides analytical and numerical analysis of the mechanisms driving concavity, including the roles of memory parameter β and reaction strength α.
- 4Demonstrates that the model can be interpreted through the lens of latent liquidity and contrarian trading behavior.
- 5Offers a parsimonious and explainable alternative to more complex LOB simulators, with computational efficiency.
Methods
- MNon-Markovian extension of the Zero Intelligence model with logistic probability for limit order signs dependent on exponentially weighted mid-price return.
- MNumerical simulations calibrated on Tesla LOB data from LOBSTER (January 5, 2015) to estimate model parameters and validate market impact dynamics.
- MAnalytical derivation of master equations for mid-price and spread evolution between child market orders.
- MStationary regime analysis linking the exponentially weighted return to the slope of the mid-price trajectory.
Results
- RThe NMZI model produces a concave price path during metaorder execution, followed by exponential decay after execution ends, consistent with empirical observations.
- RThe concavity arises from the interplay between the direct impact of child market orders and the indirect impact due to changes in limit order sign probabilities.
- RThe stationary slope of the mid-price during execution is determined by the reaction strength α and the memory parameter β.
- RThe model's response function is no longer constant; it increases with lag, unlike the flat response of the standard ZI model.
- RThe price decay after execution is exponential, with a characteristic time scale related to β.
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