High-frequency volatility of volatility estimation free from spot volatility estimates

Abstract

We define a new consistent estimator of the integrated volatility of volatility based only on a pre-estimation of the Fourier coefficients of the volatility process. We investigate the finite sample properties of the estimator in the presence of noise contaminations by computing the bias of the estimator due to noise and showing that it vanishes as the number of observations increases, under suitable assumptions. In both simulated and empirical studies, the performance of the Fourier estimator with high-frequency data is investigated and it is shown that the proposed estimator of volatility of volatility is easily implementable, computationally stable and even robust to market microstructure noise.

Keywords:

• Stochastic volatility
• Volatility of volatility
• High-frequency data
• Microstructure
• Fourier analysis

JEL Classifications:

• C13
• C14
• C58
• C22

Acknowledgements

We wish to thank Frederi Viens and an anonymous referee for their insightful comments and remarks. We thank the participants in the 5th Annual Modeling High Frequency Data in Finance conference at Stevens Institute, NJ, USA, in October 2013, for their interesting and stimulating discussion.

Notes

No potential conflict of interest was reported by the authors.