Modeling Order-Flow Price Impact with Mixture Transition Distributions

Summary

This paper models how sequences of order-flow events affect asset prices. It extends earlier impact models that treated order flow as exogenous and summarized it mainly through pairwise correlations. Instead, it represents order flow directly as a discrete process, distinguishing price-changing from non-price-changing events and combining those categories with order signs to form a four-state variable.

A Mixture Transition Distribution model provides a parsimonious approximation to a high-order Markov chain. The authors report that it captures conditional correlations between signed events and reproduces signature plots for both small-tick and large-tick stocks. They also describe a flexible calibration method for models with many parameters. Out-of-sample analysis is presented as evidence against overfitting, though the document does not give detailed datasets, evaluation metrics, or trading-performance results.

Key ideas

• The model treats order flow as a sequence of discrete events rather than an exogenous process described only by pairwise correlations.
• Price-changing status and order sign define a four-state representation of order flow.
• Mixture Transition Distributions approximate high-order Markov dynamics with a parsimonious structure.
• The model is reported to capture signed-event correlations and signature plots across different tick-size settings.
• Out-of-sample analysis is used to assess whether the many-parameter model overfits.

Tags

# Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model


# Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model









Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order flow. However, impact models presented in Part I consider the order flow as an exogenous process, only characterized by its two-point correlations. This assumption seriously limits the forecasting ability of the model. Here we attempt to model directly the stream of discrete events with a so-called Mixture Transition Distribution (MTD) framework, introduced originally by Raftery (1985). We distinguish between price-changing and non price-changing events and combine them with the order sign in order to reduce the order flow dynamics to the dynamics of a four-state discrete random variable. The MTD represents a parsimonious approximation of a full high-order Markov chain. The new approach captures with adequate realism the conditional correlation functions between signed events for both small and large tick stocks and signature plots. From a methodological viewpoint, we discuss a novel and flexible way to calibrate a large class of MTD models with a very large number of parameters. In spite of this large number of parameters, an out-of-sample analysis confirms that the model does not overfit the data.

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