Assessing the Performance of Different Volatility Estimators: A Monte Carlo Analysis

Abstract

We test the performance of different volatility estimators that have recently been proposed in the literature and have been designed to deal with problems arising when ultra high-frequency data are employed: microstructure noise and price discontinuities. Our goal is to provide an extensive simulation analysis for different levels of noise and frequency of jumps to compare the performance of the proposed volatility estimators. We conclude that the maximum likelihood estimator filter (MLE-F), a two-step parametric volatility estimator proposed by Cartea and Karyampas (2011a; The relationship between the volatility returns and the number of jumps in financial markets, SSRN eLibrary, Working Paper Series, SSRN), outperforms most of the well-known high-frequency volatility estimators when different assumptions about the path properties of stock dynamics are used.

Key Words:

• Volatility
• high-frequency data
• jumps
• microstructure noise

Acknowledgements

The authors are grateful to G. Amromin, D. Amengual, P. E. George, J. Penalva, J. Maheu, T. McCurdy, Z. Psaradakis, A. Rubia, J. Saúl, J. van Bommel and E. Schwartz for their comments. Karyampas is grateful to Birkbeck College Research Committee and the Economic & Social Research Council for financial support. This article has benefited from the comments of seminar participants at The University of Chicago, Federal Reserve Bank Chicago, University of Oxford, ESSEC. The views expressed in this article are those of the authors and do not reflect those of Credit Suisse AG.

Notes

¹ All estimators assume that data are regularly spaced when in fact they are not. Thus, the approach is to pick a time-step, for instance, 1 minute, and choose observations that are closest to that time-step.

² In this article, the efficient log-price is the log of the price of the stock without microstructure noise. In the literature, there are different ways of referring to the efficient price, such as latent price, fundamental price and true price.

³ We are assuming that once the jumps are removed what is left is Brownian motion plus (Gaussian) microstructure noise.

⁴ When , the -stable motion is the well-known standard Brownian motion (see Samorodnitsky and Taqqu (1994) and for applications in finance see Cartea and Howison (2009)).

⁵ To calculate the RMSE in this particular case we use, for each day, the mean of the realized variance given by the Heston model.

⁶ Recall that when the -stable motion becomes a Brownian motion (see Samorodnitsky and Taqqu, 1994).