communication: The Mixture Transition Distribution model for market impact and price dynamics .
speaker: Giacomo Bormetti (Scuola Normale Superiore, Pisa)speaker: Jean-Philippe Bouchaud
speaker: Fabrizio Lillo (Università di Bologna)
speaker: Damian Eduardo Taranto
speaker: Bence Toth
abstract: Market impact is a key measure in the study of financial markets. For this reason several models have been proposed in literature. In this paper we review the linear models for the impact of order flow on prices, in particular the transient and the history dependent impact models. These models posits that the price at high frequency time scales is a linear combination of past realization of the order flow, weighted by propagator functions. The propagator function is the impact of past trades on the present price. Clearly, however, prices are influenced not only by the past order flow, but also by the past realization of returns. This is particularly evident in the case of large tick stocks, where the events of price change are very rare and very informative. In the first part of the paper we extend the transient impact model in order to take into account this effect, with the introduction of two propagator functions. This extension introduces a four states discrete random variable, which is the generalization of the order signs to the case of many events. We then propose the Mixture Transition Distribution framework, introduced originally by Raftery (1985), in order to model the joint dynamics of price and trades. This model represents a parsimonious approximation of a full highorder Markov chain. We propose two versions of the model: The first one has a small number of parameters and can be estimated via Maximum Likelihood. The second one has a large number of parameters and can be estimated by the Generalized Method of Moments and we prove that the optimization problem related to this estimation is convex. We show the results of the out-of-sample prediction of the previous models, and we conclude that the second version of model, despite the higher number of parameters, is able to better capture the dynamics of the markets without overfitting of the data.
<< Go back