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A second-order stock market model

Author

Listed:
  • Robert Fernholz
  • Tomoyuki Ichiba
  • Ioannis Karatzas

Abstract

A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them appropriate as a backdrop for the analysis of the idiosyncratic behavior of individual stocks. Methods for the estimation of the parameters of second-order models are developed in this paper. Copyright Springer-Verlag 2013

Suggested Citation

  • Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Annals of Finance, Springer, vol. 9(3), pages 439-454, August.
    • Handle: RePEc:kap:annfin:v:9:y:2013:i:3:p:439-454
    DOI: 10.1007/s10436-012-0193-2
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    References listed on IDEAS

    as
    1. Mitchel Y. Abolafia (ed.), 2005. "Markets," Books, Edward Elgar Publishing, number 2788.
    2. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
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    Citations

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    Cited by:

    1. Sergey Sosnovskiy, 2015. "On financial applications of the two-parameter Poisson-Dirichlet distribution," Papers 1501.01954, arXiv.org, revised Jul 2015.
    2. David Itkin & Martin Larsson, 2024. "Calibrated rank volatility stabilized models for large equity markets," Papers 2403.04674, arXiv.org.
    3. Kangjianan Xie, 2020. "Leakage of rank-dependent functionally generated trading strategies," Annals of Finance, Springer, vol. 16(4), pages 573-591, December.
    4. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Post-Print hal-00921151, HAL.
    5. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Oct 2024.
    6. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    7. Benjamin Jourdain & Julien Reygner, 2013. "Capital distribution and portfolio performance in the mean-field Atlas model," Papers 1312.5660, arXiv.org, revised Aug 2014.
    8. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    9. Sergey Sosnovskiy, 2015. "Market shape formation, statistical equilibrium and neutral evolution theory," Papers 1506.07163, arXiv.org.

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    More about this item

    Keywords

    Stochastic portfolio theory; Atlas model; First-order model; Second-order model; G10;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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