Open Access
November 2015 Estimation of integrated volatility of volatility with applications to goodness-of-fit testing
Mathias Vetter
Bernoulli 21(4): 2393-2418 (November 2015). DOI: 10.3150/14-BEJ648


In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on increments of spot volatility estimators. Some of those are positive by construction, others are bias corrected in order to attain the optimal rate $n^{-1/4}$. Associated central limit theorems are proven which can be widely used in practice, as they are the key to essentially all tools in model validation for stochastic volatility models. As an illustration we give a brief idea on a goodness-of-fit test in order to check for a certain parametric form of volatility of volatility.


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Mathias Vetter. "Estimation of integrated volatility of volatility with applications to goodness-of-fit testing." Bernoulli 21 (4) 2393 - 2418, November 2015.


Received: 1 July 2012; Revised: 1 March 2014; Published: November 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1125.62084
MathSciNet: MR3378471
Digital Object Identifier: 10.3150/14-BEJ648

Keywords: central limit theorem , goodness-of-fit testing , high-frequency observations , model validation , stable convergence , stochastic volatility model

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 4 • November 2015
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