Are volatility estimators robust with respect to modeling assumptions?

Details Are volatility estimators robust with respect to modeling assumptions? Are volatility estimators robust with respect to modeling assumptions?

2007-09-04

arxiv.org/abs/0709.0440v1

Bernoulli 2007, Vol. 13, No. 3, 601-622

Economy

Quantitative Finance

Statistical Finance

Published at http://dx.doi.org/10.3150/07-BEJ6067 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6067

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 is robust to the form of contamination $Q$. To push the limits of our result, we show what happens for some models that involve 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 the use to which the estimator of volatility will be put.

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