Revisiting of Empirical Zero Intelligence Models

Vyacheslav Arbuzov

Abstract This paper describes a zero-intelligence approach implementation for the modeling of financial markets. We construct a mechanism of order flow and market engine simulation. We analyze stylized facts to estimate the quality of our models. The research is based on a 1 month order and execution history data of the Moscow Exchange (MOEX) for one stock (JSC “Aeroflot”).

Keywords Daniels model • Market microstructure • Mike-Farmer model • Order flow • Stylized facts • Tail exponent • Zero-intelligence models

JEL Classification G15, G17

1 Introduction

Agent-based models play an important role in understanding the mechanisms of financial markets driven by the advances in technologies that allow the creation and calibration of complex and very detailed models. An adequate replication of the mechanism of the price formation in those models is of the same or greater importance than the replication of the behavior of the agents. As first shown in Daniels et al. (2003), zero-intelligence (ZI) agent models are able to reproduce statistical regularities of the market with the Continuous Double Auction (CDA). ZI models are based on the hypothesis that the behavior of all agents can be described by random order flow with empirically estimated parameters. We studied the implementation of a ZI model on the Russian market. We reconstructed Daniels and Mike-Farmer versions.

After the description of Farmer and Daniels models, we try to change some details in the model and compare all our models with the real market.

V. Arbuzov (H)

Department of Economics, Prognoz Risk Lab, Perm State National Research University, Perm, Russia

e-mail: arbuzov@prognoz. ru; arbuzov1989@gmail. com © Springer International Publishing Switzerland 2015

A. K. Bera et al. (eds.), Financial Econometrics and Empirical Market

Microstructure, DOI 10.1007/978-3-319-09946-0_____ 3

2 Data

Our study is based on detailed market data, which includes the order history (order log) for Aeroflot stock (AFLT). Aeroflot is the largest Russian airline company and its equity is referred to as blue chip and is included in the MICEX index. During the observed period (21 trading days) there were, 2,765,074 orders which arrived and 31,572 which were executed (15,786 trades). Over this period, 15.3 million stocks were bought and sold yielding a 779.4 million ruble (approximately $26 million) turnover. All the data comes from the Moscow Exchange and is based in Perm State National Research University clusters (Computer cluster for reverse engineering, agent-based modeling and market microstructure researches of the Russian capital market). Most calculations were made using statistical environment R (Core Team R 2013). For calculations of the best bid and best asking prices from the order flow we used an Rcpp package with low-level programming.

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