  We analyze the empirical performance of several non-parametric estimators of
the pricing functional for European options, using historical put and call
prices on the S&P500 during the year 2012. Two main families of estimators are
considered, obtained by estimating the pricing functional directly, and by
estimating the (Black-Scholes) implied volatility surface, respectively. In
each case simple estimators based on linear interpolation are constructed, as
well as more sophisticated ones based on smoothing kernels, \`a la
Nadaraya-Watson. The results based on the analysis of the empirical pricing
errors in an extensive out-of-sample study indicate that a simple approach
based on the Black-Scholes formula coupled with linear interpolation of the
volatility surface outperforms, both in accuracy and computational speed, all
other methods.
