A long-range memory stochastic model of the return in financial markets

V. Gontis, J. Ruseckas and A. Kononovičius

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 1, 100-106

Abstract: We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.

Keywords: Models of financial markets; Stochastic equations; Power law distributions; Long memory processes (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:1:p:100-106

DOI: 10.1016/j.physa.2009.09.011

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