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Volatility Is Log-Normal—But Not for the Reason You Think

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  • Martin Tegnér

    (Department of Engineering & Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford OX1 3PJ, UK)

  • Rolf Poulsen

    (Department of Mathematical Sciences, University of Copenhagen, 2100 København Ø, Denmark)

Abstract

It is impossible to discriminate between the commonly used stochastic volatility models of Heston, log-normal, and 3-over-2 on the basis of exponentially weighted averages of daily returns—even though it appears so at first sight. However, with a 5-min sampling frequency, the models can be differentiated and empirical evidence overwhelmingly favours a fast mean-reverting log-normal model.

Suggested Citation

  • Martin Tegnér & Rolf Poulsen, 2018. "Volatility Is Log-Normal—But Not for the Reason You Think," Risks, MDPI, vol. 6(2), pages 1-16, April.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:46-:d:143022
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    References listed on IDEAS

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    Cited by:

    1. Miriam Hägele & Jaakko Lehtomaa, 2021. "Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance," JRFM, MDPI, vol. 14(5), pages 1-18, May.
    2. Alan L. Lewis, 2018. "Exact Solutions for a GBM-type Stochastic Volatility Model having a Stationary Distribution," Papers 1809.08635, arXiv.org, revised May 2019.
    3. Kim, See-Woo & Kim, Jeong-Hoon, 2019. "Variance swaps with double exponential Ornstein-Uhlenbeck stochastic volatility," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 149-169.

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