Non Parametric Estimates of Option Prices Using Superhedging

Abstract

We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As an application we first test the methodology on a simulated sample of option prices and then on the S\&P 500 index options.