Estimating State Price Densities via Local Polynomials

Abstract

This master thesis aims at estimating state price densities (SPD) via a nonparametric fit of the implied volatility smile and of its derivatives. To achieve this task, we use the local polynomial estimators and apply the empirical bias-bandwidth selector (EBBS) algorithm to determine both global and local optimal bandwidths. The accuracy of the nonparametric estimates is then studied from the statistical and financial points of view. Afterwards, the resulting SPD estimates are presented as well as their bootstrap confidence bands. In a last part, we compare our semiparametric method with the implied binomial trees.