Modeling long-range memory trading activity by stochastic differential equations

Details Modeling long-range memory trading activity by stochastic differential equations Modeling long-range memory trading activity by stochastic differential equations

2006-08-03

arxiv.org/abs/physics/0608036v1

Physics

Physics and Society

12 pages, 4 figures, APFA5 Proceedings

Scientific paper

10.1016/j.physa.2007.02.012

We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets. We present a simple stochastic relation between the trading activity and return, which enables us to reproduce long-range memory statistical properties of volatility by numerical calculations based on the proposed fractal point process.

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