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A Model for Stock Returns and Volatility

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  • 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
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    File URL: http://arxiv.org/pdf/1305.4173
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    References listed on IDEAS

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    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. Anonymous, 1993. "Arer Reviewers, June 1992 To May 1993," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 22(2), October.
    4. Cep, 1993. "Annual Review 92-93," CEP Discussion Papers dp0174, Centre for Economic Performance, LSE.
    5. Anonymous, 1993. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 37(03), December.
    6. Anonymous, 1993. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 37(02), August.
    7. Anonymous, 1993. "Book Reviews," Journal of Agricultural Cooperation, National Council of Farmer Cooperatives, vol. 8.
    8. Anonymous, 1993. "Book Reviews," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 61(03), December.
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    Cited by:

    1. 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.

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