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Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

Author

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  • Moawia Alghalith

    (Department of Economics, University of West Indies, St. Augustine, Trinidad, Trinidad and Tobago)

  • Christos Floros

    (Department of Accounting & Finance, School of Economics & Management Sciences, Hellenic Mediterranean University, Heraklion 71410, Greece)

  • Konstantinos Gkillas

    (Department of Business Administration, University of Patras, Patras 26500, Greece)

Abstract

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasonably accurate. Such evidence implies that the stochastic volatility models proposed in the literature with constant volatility of volatility may fail to approximate the discrete-time short rate dynamics.

Suggested Citation

  • Moawia Alghalith & Christos Floros & Konstantinos Gkillas, 2020. "Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility," Risks, MDPI, vol. 8(2), pages 1-15, April.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:2:p:35-:d:344228
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    References listed on IDEAS

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    Cited by:

    1. Christos Floros & Konstantinos Gkillas & Christoforos Konstantatos & Athanasios Tsagkanos, 2020. "Realized Measures to Explain Volatility Changes over Time," JRFM, MDPI, vol. 13(6), pages 1-19, June.
    2. Loretta Mastroeni, 2022. "Pricing Options with Vanishing Stochastic Volatility," Risks, MDPI, vol. 10(9), pages 1-16, September.
    3. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.

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