Robust European Call Option Pricing via Linear Regression

The one-period trinomial option pricing model is well known in the literature as it considers three possible movement directions of the asset price. However, by equating the price of the option with the self-financing hedging portfolio at maturity, this yields a linear system of three equations with two unknowns that correspond to the coefficients for the delta hedging portfolio. Hence, the trinomial model is said to be incomplete, that is, there exists an infinite number of equivalent martingale measures. To deal with this incompleteness, this paper aims to price options via some robust linear regression techniques in order to mainly handle the problem of outliers that the least squares fails to consider. The proposed robust techniques are evaluated on numerical data, the results of which demonstrate their effectiveness for European call option pricing.