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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.

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  • 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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    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.

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