Modeling the inverse cubic distributions by nonlinear stochastic differential equations

Abstract

One of stylized facts emerging from statistical analysis of financial markets is the inverse cubic law for the cumulative distribution of a number of events of trades and of the logarithmic price change. A simple model, based on the point process model of 1/f noise, generating the long-range processes with the inverse cubic cumulative distribution is proposed and analyzed. Main assumptions of the model are proportional to the process intensity, 1/τ(t), stochasticity of large interevent time τ(t) and the Brownian motion of small interevent time.