Financial Econometrics and Empirical Market Microstructure

Modeling Financial Market Using Percolation Theory

Anastasiya Byachkova and Artem Simonov

Abstract Econophysics is a relatively new discipline. It is one of the most interesting and promising trends in modeling complex economic systems such as financial markets. In this paper we use the approach of econophysics to explain various mechanisms of price formation in the stock market. We study a model, which was proposed by Jean-Philippe Bouchaud and Dietrich Stauffer (Bouchaud 2002; Chang et al. 2002; Stauffer 2001; Stauffer and Sornette 1990), and used to describe the agents’ cooperation in the market. The most important point of this research is the calibration of the model, using real market conditions to proof the model’s possibility of setting out a real market pricing process.

Keywords Agent modeling • Econophysics • Financial markets modeling • Percolation theory • Quantitative finance

1 Elements of the Percolation Theory

Physics and finance are both based on the theory of random walks and on the collective behavior of large numbers of correlated variables (Sornette et al. 1999).

The considered model is based on percolation theory, which describes phase transition in physical systems. It regards the square lattice fromL * L sites. Every site can be “occupied” or “free”; the site can be occupied with probability p randomly. The groups of neighboring occupied sites are formed in clusters.

The main task of the percolation theory is to search for an infinite cluster— cluster, which extends from one side of the lattice to another. In this situation, most parts of cells belong to one cluster. In this case pc is the percolation threshold, the critical probability of infinite cluster appearance and the offensive of phase

A. Byachkova (H)

JSC Prognoz,, Perm, Russia e-mail: abyachkova@gmail. com

A. Simonov

EY Advisory, Moscow, Russia e-mail: art. simonov@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_____ 5 transition (Gould and Tobochnik 1990). Next, we turn to the application of the model in finance.