Are Volatility Estimators Robust with Respect to Modeling Assumptions

By Yingying Li, Per Aslak Mykland. 2007

72 citations recorded by the source corpus.

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel Q. Special cases include additive error, rounding, and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility (TSRV) is robust to the form of contamination Q. To push the limits of our result, we show what happens for some models involving rounding (which is not, of course, smooth) and see in this situation how the robustness deteriorates with decreasing smoothness. Our conclusion is that under reasonable smoothness, one does not need to consider too closely how the microstructure is formed, while if severe non-smoothness is suspected, one needs to pay attention to the precise structure and also to what use the estimator of volatility will be put.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/b8b5eeb84eab239a52d5b2b797aa32b73f0beb9e

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Citations in the corpus

Integrated volatility and round-off error (2009, unknown): “= E[|Z|].”
VOLATILITY AND COVARIATION ESTIMATION WHEN MICROSTRUCTURE NOISE AND TRADING TIMES ARE ENDOGENOUS (2012, background): “More convincing types of microstructure noise are given by the cases of a contamination of the ecient price through a Markov kernel ([23], [ 27 ]) and a rounding error ([9], [26], [32]).”
Statistical Properties of Microstructure Noise (2013, unknown): “Gloter and Jacod (2001), Li and Mykland (2007) and Rosenbaum (2009) studied the case when the noise is of specific form such as roundoff errors or round-off errors on top of additive white noise.”
Microstructure Noise in the Continuous Case: The Pre-Averaging Approach ∗ (2008, unknown): “In the nonparametric setting, the deviation from semimartigales is most clearly seen through the signature plots of Andersen et al. (2000), see also the discussion in Mykland and Zhang (2005).”
The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency (2011, background): “Related work include Bandi and Russell (2006), Delattre and Jacod (1997), Fan andWang (2007), Gatheral and Oomen (2010), Hansen and Lunde (2006), Kalnina and Linton (2008), Li and Mykland (2007), Aı̈t-Sahalia et al. (2011) and Li et al. (2010).”
Realized kernels in practice: trades and quotes (2009, methodology): “Specific models for U have been suggested in this context by, for example, Zhou (1996), Hansen and Lunde (2006), Li and Mykland (2007), and Diebold and Strasser (2007).”
Testing for jumps in noisy high frequency data (2012, background): “Attempting to generalize the type of noise allowed to an ''unsmooth'' setting raises a different set of issues that are beyond the scope of this paper (see Li and Mykland (2007) for a discussion).”
Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data (2010, background): “Related work includes Bandi and Russell (2006), Delattre and Jacod (1997), Fan and Wang (2007), Gatheral and Oomen (2010), Hansen and Lunde (2006), Kalnina and Linton (2008), Li and Mykland (2007), AïtSahalia, Mykland, and Zhang (2011), and Li et al. (2010). etc.”
Limit theorems for moving averages of discretized processes plus noise (2010, background): “A comprehensive discussion of the noise models and the effect of noise on the inference for the underlying process may be found in [12].”
Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error (2008, background): “Other examples where the inference question needs to be solved include autocorrelation in measurement error (as in AïtSahalia et al. (2006a)), or other generalizations to the independent additive error model (Li and Mykland, 2007).”
Quasi-maximum likelihood estimation of volatility with high frequency data (2010, background): “Li and Mykland (2007) have discussed the robustness of the TSRV with respect to rounding errors while Jacod et al. (2007) have recently proposed a pre-averaging approach that works well for a general class of errors including certain combination of rounding and additive errors.”