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Two-dimensional stochastic dynamics as model for time evolution of the financial market

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  • Lima, L.S.
  • Oliveira, S.C.

Abstract

The dynamical model of coupled prices in the financial market is proposed based in a set of coupled stochastic differential equations where we assume there are two stocks, each with stochastic differential equation. These stocks are typically correlated. We analyse stylized facts observed in the financial markets as the long-tail distribution of the probability density of the returns and verified if the long tail of probability density distribution obeys to a scale law obeyed by the financial markets and therefore, if the model is adequate for the financial market. Furthermore, we obtain the behavior of the long range memory of the time series of the model and derive the correspondent Black-Scholes equation for the value of a European call.

Suggested Citation

  • Lima, L.S. & Oliveira, S.C., 2020. "Two-dimensional stochastic dynamics as model for time evolution of the financial market," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920301946
    DOI: 10.1016/j.chaos.2020.109792
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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
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    Cited by:

    1. Wang, Zhuo & Shang, Pengjian, 2021. "Generalized entropy plane based on multiscale weighted multivariate dispersion entropy for financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Xu, Chao & Zhao, Xiaojun & Wang, Yanwen, 2022. "Causal decomposition on multiple time scales: Evidence from stock price-volume time series," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Fonseca, Carla L.G. & de Resende, Charlene C. & Fernandes, Danilo H.C. & Cardoso, Rodrigo T.N. & de Magalhães, A.R. Bosco, 2021. "Is the choice of the candlestick dimension relevant in econophysics?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).

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