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Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

1
Department of Economics, University of West Indies, St. Augustine, Trinidad, Trinidad and Tobago
2
Department of Accounting & Finance, School of Economics & Management Sciences, Hellenic Mediterranean University, Heraklion 71410, Greece
3
Department of Business Administration, University of Patras, Patras 26500, Greece
*
Author to whom correspondence should be addressed.
Risks 2020, 8(2), 35; https://doi.org/10.3390/risks8020035
Received: 12 March 2020 / Revised: 7 April 2020 / Accepted: 9 April 2020 / Published: 11 April 2020
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. View Full-Text
Keywords: nonparametric estimators; stochastic volatility; stochastic volatility of volatility nonparametric estimators; stochastic volatility; stochastic volatility of volatility
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Alghalith, M.; Floros, C.; Gkillas, K. Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility. Risks 2020, 8, 35.

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