  We propose model-free (nonparametric) estimators of the volatility of
volatility and leverage effect using high-frequency observations of short-dated
options. At each point in time, we integrate available options into estimates
of the conditional characteristic function of the price increment until the
options' expiration and we use these estimates to recover spot volatility. Our
volatility of volatility estimator is then formed from the sample variance and
first-order autocovariance of the spot volatility increments, with the latter
correcting for the bias in the former due to option observation errors. The
leverage effect estimator is the sample covariance between price increments and
the estimated volatility increments. The rate of convergence of the estimators
depends on the diffusive innovations in the latent volatility process as well
as on the observation error in the options with strikes in the vicinity of the
current spot price. Feasible inference is developed in a way that does not
require prior knowledge of the source of estimation error that is
asymptotically dominating.
