IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1305.4173.html
   My bibliography  Save this paper

A Model for Stock Returns and Volatility

Author

Listed:
  • Tao Ma
  • R. A. Serota

Abstract

We prove that Student's t-distribution provides one of the better fits to returns of S&P component stocks and the generalized inverse gamma distribution best fits VIX and VXO volatility data. We further argue that a more accurate measure of the volatility may be possible based on the fact that stock returns can be understood as the product distribution of the volatility and normal distributions. We find Brown noise in VIX and VXO time series and explain the mean and the variance of the relaxation times on approach to the steady-state distribution.

Suggested Citation

  • Tao Ma & R. A. Serota, 2013. "A Model for Stock Returns and Volatility," Papers 1305.4173, arXiv.org.
    • Handle: RePEc:arx:papers:1305.4173
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1305.4173
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. N/A, 1993. "Book Review Index," Environment and Planning A, , vol. 25(12), pages 1853-1856, December.
    2. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Unknown, 1993. "Book Reviews," Journal of Agricultural Cooperation, National Council of Farmer Cooperatives, vol. 8, pages 1-8.
    4. Unknown, 1993. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 37(3), pages 1-10, December.
    5. Unknown, 1993. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 37(2), pages 1-22, August.
    6. Unknown, 1993. "Book Reviews," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 61(03), pages 1-5, December.
    7. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    8. Unknown, 1993. "Arer Reviewers, June 1992 To May 1993," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 22(2), pages 1-1, October.
    9. Cep, 1993. "Annual Review 92-93," CEP Discussion Papers dp0174, Centre for Economic Performance, LSE.
    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. Fahad Mostafa & Pritam Saha & Mohammad Rafiqul Islam & Nguyet Nguyen, 2021. "GJR-GARCH Volatility Modeling under NIG and ANN for Predicting Top Cryptocurrencies," JRFM, MDPI, vol. 14(9), pages 1-22, September.
    2. Larson, James F. & Park, Jaemin, 2014. "From developmental to network state: Government restructuring and ICT-led innovation in Korea," Telecommunications Policy, Elsevier, vol. 38(4), pages 344-359.
    3. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching to nonaffine stochastic volatility: a closed-form expansion for the Inverse Gamma model," Post-Print hal-02909113, HAL.

    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. Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Distributional Mellin calculus in $\mathbb{C}^n$, with applications to option pricing," Papers 1611.03239, arXiv.org, revised Nov 2016.
    2. Gerald T. Garvey, 1994. "Why Labour Is Not Different," Agenda - A Journal of Policy Analysis and Reform, Australian National University, College of Business and Economics, School of Economics, vol. 1(1), pages 5-12.
    3. MacDougall, Gordon P., 2011. "Book Review," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 50(01).
    4. Hoffman, John R. & Rosenthal, Jeffrey S., 1995. "Convergence of independent particle systems," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 295-305, April.
    5. Newell, G. F., 1998. "The rolling horizon scheme of traffic signal control," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 39-44, January.
    6. Lamberton, Donald M., 1998. "Information economics research: Points of departure," Information Economics and Policy, Elsevier, vol. 10(3), pages 325-330, September.
    7. Ma, Tao & Serota, R.A., 2014. "A model for stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 89-115.
    8. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    9. Ma, Junmei & Wang, Chen & Xu, Wei, 2025. "A new lattice approach for risk-minimization hedging under generalized autoregressive conditional heteroskedasticity models," European Journal of Operational Research, Elsevier, vol. 321(3), pages 1021-1035.
    10. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    11. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    12. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    13. Xuemei Gao & Dongya Deng & Yue Shan, 2014. "Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-6, April.
    14. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 407-458, Fall.
    15. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    16. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    17. Pierre J. Venter & Eben Maré, 2020. "GARCH Generated Volatility Indices of Bitcoin and CRIX," JRFM, MDPI, vol. 13(6), pages 1-15, June.
    18. Bertram During & Christian Hendricks & James Miles, 2016. "Sparse grid high-order ADI scheme for option pricing in stochastic volatility models," Papers 1611.01379, arXiv.org.
    19. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    20. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Post-Print halshs-00469529, HAL.

    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:1305.4173. 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.