Linear Models for the Impact of Order Flow on Prices II. The Mixture Transition Distribution Model

Abstract

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.

Dissecting cross-impact on stock markets: an empirical analysis

“…The behavior at negative lag indicates that the current return allows some prediction of the sign imbalance, an effect that has been extensively investigated in Refs. [31,33]. § It is worth mentioning that, other than the expected amplitude difference, the off-diagonal response shows the same temporal behaviour than its diagonal counterpart.…”

“…(6) § We will disregard in the following the behavior of returns at negative lags, and only focus on the positive part of the curve, that is equivalent to assuming no price-sign correlation, that is approximately correct for small tick stocks, and breaks down at high frequency and for large tick stocks due to microstructural effects [31,33,34]. This expresses the price variations of contract i as a linear regression on the past sign imbalances of all assets j.…”

A continuous and efficient fundamental price on the discrete order book grid

“…Therefore, our work contributes significantly to the understanding of the interplay between liquidity provision and consumption in financial markets. Superficially, this aspect of our study resembles Hasbrouck [1991]'s vector regression model of price returns and order flow and its recent generalization to large tick stocks [Taranto et al, 2016b]. While we are able to infer directly the correlation between trade and public information shocks by using the proxy of the fundamental price, Hasbrouck [1991] performs an regression on price returns and order flow omitting the effect of public information shocks.…”

A Continuous and Efficient Fundamental Price on the Discrete Order Book Grid

“…Therefore, our work contributes significantly to the understanding of the interplay between liquidity provision and consumption in financial markets. Superficially, this aspect of our study resembles Hasbrouck [1991]'s vector regression model of price returns and order flow and its recent generalization to large tick stocks [Taranto et al, 2016b]. While we are able to infer directly the correlation between trade and public information shocks by using the proxy of the fundamental price, Hasbrouck [1991] performs an regression on price returns and order flow omitting the effect of public information shocks.…”