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Distributions of historic market data: relaxation and correlations

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  • M. Dashti Moghaddam

    (University of Cincinnati)

  • Zhiyuan Liu

    (University of Cincinnati)

  • R. A. Serota

    (University of Cincinnati)

Abstract

We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models— multiplicative, Heston (Cox-Ingersoll-Ross) and combined multiplicative-Heston—whose steady-state probability density functions are Gamma, Inverse Gamma and Beta Prime respectively, the latter two exhibiting “fat” tails. For the Heston model, we apply the eigenvalue analysis of the Fokker-Planck equation to derive the correlation function—in agreement with the general analysis— and to identify a series of time scales, which are observable in relaxation of cumulants on approach to the steady state. We test our findings on a very large set of historic financial markets data. Graphic abstract

Suggested Citation

  • M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2021. "Distributions of historic market data: relaxation and correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(4), pages 1-13, April.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:4:d:10.1140_epjb_s10051-021-00089-9
    DOI: 10.1140/epjb/s10051-021-00089-9
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