https://doi.org/10.1140/epjb/e2007-00185-4
Interacting gaps model, dynamics of order book, and stock-market fluctuations
1
Department of Theoretical Physics and Didactics of Physics, FMFI, Comenius University, Mlynska Dolina, 84248 Bratislava, Slovakia
2
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Praha, Czech Republic and Center for Theoretical Study, Jilská 1, Prague, Czech Republic
Corresponding author: a slanina@fzu.cz
Received:
13
December
2006
Revised:
15
May
2007
Published online:
29
June
2007
Inspired by order-book models of financial fluctuations, we investigate the Interacting gaps model, which is the schematic one-dimensional system mimicking the order-book dynamics. We find by simulations the power-law tail in return distribution, power-law decay of volatility autocorrelation with exponent 0.5 and Hurst exponent close to 1/2. Surprisingly, when we make a mean-field approximation, i.e. replace the one-dimensional system by effectively infinite-dimensional one, we obtain analytically the return exponent 5/2, in perfect accord with one-dimensional simulations.
PACS: 89.65.-s – Social and economic systems / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007
