  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.
