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Exogenous shock and multifractal random walk

Author

Listed:
  • Koji Kuroda

    (Nihon University)

  • Jun-ichi Maskawa

    (Seijo University)

Abstract

We construct a log-volatility process for Multifractal Random Walk from a discrete time model as a scale limit and consider an exogenous shock and the relaxation process of the volatility. In this construction, taking an effect of exogenous shock into account, we consider a model for trades transacted by traders with different investment time horizons. Using the method of cluster expansion developed in mathematical physics, we obtain the convergence of scale limit of log-volatility process. For this scale limit, we prove the relaxation of the volatility after exogenous shock is given by an inverse power law $$\frac{1}{t^\delta }$$ 1 t δ with exponent $$\delta =1$$ δ = 1 .

Suggested Citation

  • Koji Kuroda & Jun-ichi Maskawa, 2019. "Exogenous shock and multifractal random walk," Evolutionary and Institutional Economics Review, Springer, vol. 16(1), pages 213-238, June.
    • Handle: RePEc:spr:eaiere:v:16:y:2019:i:1:d:10.1007_s40844-018-0106-9
    DOI: 10.1007/s40844-018-0106-9
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    References listed on IDEAS

    as
    1. Stošić, Dusan & Stošić, Darko & Stošić, Tatijana & Eugene Stanley, H., 2015. "Multifractal properties of price change and volume change of stock market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 46-51.
    2. Koji Kuroda, 2016. "Investment time horizon and multifractality of stock price process," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 481-496, December.
    3. Armand Joulin & Augustin Lefevre & Daniel Grunberg & Jean-Philippe Bouchaud, 2008. "Stock price jumps: news and volume play a minor role," Papers 0803.1769, arXiv.org.
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    Cited by:

    1. Yuichi Ikeda, 2019. "Special feature: Econophysics 2017: synergetic fusion of econophysics and other fields of science—Part II," Evolutionary and Institutional Economics Review, Springer, vol. 16(1), pages 181-182, June.

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    More about this item

    Keywords

    Exogenous shock; Multifractal; Investment time horizon; Abstract polymer expansion;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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