Nonparametric Estimates of Option Prices and Related Quantities

We propose a new nonparametric technique to estimate the call function based on the superhedging principle. This approach requires minimal assumptions on absence of arbitrage and other market imperfections. The estimates so obtained are then combined with SNP estimates of the actual density of market returns. This permits to investigate the time behavior of the relative distance between the two densities obtained. Our empirical findings suggest that the more the two densities differ, the shorter is time to maturity, suggesting a major role of uncertainty over shorter than longer horizons.