Before revision: In quantitative finance, we often wish to recover the volatility of asset prices given by a noisy It\=o semimartingale. Existing estimates, however, lose accuracy when the jumps are of infinite variation, as is suggested by empirical evidence .
After revision: In quantitative finance, we often wish to recover the volatility of asset prices given by a noisy Ito semimartingale; unfortunately, this model is too complex to identify from price data .