Modelling financial markets by the multiplicative sequence of trades

Abstract

We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law probability distribution of the trading activity. The model reproduces the spectral properties of trading activity and explains the mechanism of power-law distribution in real markets.

arXiv comment6 pages, 2 figures

References in corpus (6)

• Inverse Cubic Law for the Probability Distribution of Stock Price Variations
• Statistical Properties of Share Volume Traded in Financial Markets
• Power Laws are Logarithmic Boltzmann Laws
• Modeling 1/f noise
• Autoregressive model of 1/f noise
• Multiplicative Stochastic Model of the Time Interval between Trades in Financial Markets

Cited by in corpus (11)

• Point process model of 1/f noise versus a sum of Lorentzians
• Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations
• Nonlinear stochastic models of 1/f noise and power-law distributions
• Modeling long-range memory trading activity by stochastic differential equations
• Trading activity as driven Poisson process: comparison with empirical data
• Long-range memory model of trading activity and volatility
• Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets
• Order flow in the financial markets from the perspective of the Fractional Lévy stable motion
• Spurious memory in non-equilibrium stochastic models of imitative behavior
• Understanding the nature of the long-range memory phenomenon in socioeconomic systems
• Long-range memory test by the burst and inter-burst duration distribution