Modeling long-range memory trading activity by stochastic differential equations

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...

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Bibliographic Details
Published inIDEAS Working Paper Series from RePEc
Main Authors Gontis, V, Kaulakys, B
Format Paper
LanguageEnglish
Published St. Louis Federal Reserve Bank of St. Louis 01.01.2006
Subjects
Fractals
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Summary: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.