Nonparametric estimates of pricing functionals

TL;DR

This paper compares various non-parametric methods for estimating European option pricing functionals, finding that simple linear interpolation of the implied volatility surface within the Black-Scholes framework performs best empirically.

Contribution

It provides an empirical evaluation of different non-parametric estimators for option pricing, highlighting the effectiveness of a simple linear interpolation approach.

Findings

Linear interpolation of the implied volatility surface outperforms other methods in accuracy.

The simple approach is faster computationally.

Empirical results are based on S&P 500 options data from 2012.

Abstract

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.