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

23 Pages Posted: 28 Apr 2016

See all articles by Damian Taranto

Damian Taranto

Scuola Normale Superiore

Giacomo Bormetti

University of Bologna - Department of Mathematics

Jean-Philippe Bouchaud

Capital Fund Management

Fabrizio Lillo

Università di Bologna

Bence Toth

Santa Fe Institute

Date Written: April 26, 2016

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.

Keywords: Financial markets, market microstructure, market impact, liquidity, markov chain

JEL Classification: C1, G1

Suggested Citation

Taranto, Damian and Bormetti, Giacomo and Bouchaud, Jean-Philippe and Lillo, Fabrizio and Toth, Bence, Linear Models for the Impact of Order Flow on Prices II. The Mixture Transition Distribution Model (April 26, 2016). Available at SSRN: https://ssrn.com/abstract=2770363 or http://dx.doi.org/10.2139/ssrn.2770363

Damian Taranto (Contact Author)

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

Bence Toth

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States

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