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A Model for Stock Returns and Volatility


  • Tao Ma
  • R. A. Serota


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,
  • Handle: RePEc:arx:papers:1305.4173

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    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.
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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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