IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1302.3870.html
   My bibliography  Save this paper

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.

Suggested Citation

  • Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Papers 1302.3870, arXiv.org.
    • Handle: RePEc:arx:papers:1302.3870
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1302.3870
    File Function: Latest version
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Annals of Finance, Springer, vol. 9(3), pages 439-454, August.
    2. Ioannis Karatzas & Soumik Pal & Mykhaylo Shkolnikov, 2012. "Systems of Brownian particles with asymmetric collisions," Papers 1210.0259, arXiv.org.
    3. Sousa, Carlos M.P. & Bradley, Frank, 2008. "Antecedents of international pricing adaptation and export performance," Journal of World Business, Elsevier, vol. 43(3), pages 307-320, July.
    4. Barry Eichengreen & Poonam Gupta & Ashoka Mody, 2008. "Sudden Stops and IMF-Supported Programs," NBER Chapters, in: Financial Markets Volatility and Performance in Emerging Markets, pages 219-266, National Bureau of Economic Research, Inc.
    5. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    6. Christa Cuchiero, 2017. "Polynomial processes in stochastic portfolio theory," Papers 1705.03647, arXiv.org.
    7. D Büttner & B. Hayo, 2012. "EMU-related news and financial markets in the Czech Republic, Hungary and Poland," Applied Economics, Taylor & Francis Journals, vol. 44(31), pages 4037-4053, November.
    8. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    9. Goodwin, Neva, 2010. "A New Economics for the 21st Century," MPRA Paper 27907, University Library of Munich, Germany.
    10. Ravi Bansal, 2007. "Long-run risks and financial markets," Review, Federal Reserve Bank of St. Louis, vol. 89(Jul), pages 283-300.
    11. Ravi Bansal & Dana Kiku & Ivan Shaliastovich & Amir Yaron, 2014. "Volatility, the Macroeconomy, and Asset Prices," Journal of Finance, American Finance Association, vol. 69(6), pages 2471-2511, December.
    12. Lehr, Ulrike & Nitsch, Joachim & Kratzat, Marlene & Lutz, Christian & Edler, Dietmar, 2008. "Renewable energy and employment in Germany," Energy Policy, Elsevier, vol. 36(1), pages 108-117, January.
    13. Guonan Ma, 2007. "Who Pays China's Bank Restructuring Bill?," Asian Economic Papers, MIT Press, vol. 6(1), pages 46-71, Winter.
    14. David Itkin & Martin Larsson, 2021. "On A Class Of Rank-Based Continuous Semimartingales," Papers 2104.04396, arXiv.org.
    15. Connelly, Luke B. & Brown III, H. Shelton, 2008. "Lifetime Fairness? Taxes, Subsidies, Age-Based Penalties, and the Price of Health Insurance in Australia," MPRA Paper 14671, University Library of Munich, Germany.
    16. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Annals of Finance, Springer, vol. 11(2), pages 151-198, May.
    17. Paul Frijters & Robert Gregory, 2006. "From Golden Age to Golden Age: Australia's ‘Great Leap Forward’?," The Economic Record, The Economic Society of Australia, vol. 82(257), pages 207-224, June.
    18. Ricardo T. Fernholz & Robert Fernholz, 2022. "Permutation-weighted portfolios and the efficiency of commodity futures markets," Annals of Finance, Springer, vol. 18(1), pages 81-108, March.
    19. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2009. "Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5099-5131, December.
    20. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1302.3870. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.