  We address the information content of European option prices about volatility
in terms of the Fisher information matrix. We assume that observed option
prices are centred on the theoretical price provided by Heston's model
disturbed by additive Gaussian noise. We fit the likelihood function on the
components of the VIX, i.e., near- and next-term put and call options on the
S&P 500 with more than 23 days and less than 37 days to expiration and
non-vanishing bid, and compute their Fisher information matrices from the
Greeks in the Heston model. We find that option prices allow reliable estimates
of volatility with negligible uncertainty as long as volatility is large
enough. Interestingly, if volatility drops below a critical value, inferences
from option prices become impossible because Vega, the derivative of a European
option w.r.t. volatility, nearly vanishes.
