Linear Regression for Currency European Call Option Pricing in Incomplete Markets

Abstract

The least squares method is the traditional regression technique for pricing European options in incomplete markets by constructing a self-financing hedging portfolio that does not perfectly replicate the call option. However, the least squares method is quite sensitive to even a single outlier in the data, and thus the predicted option price may potentially deviate from the true unknown value. To alleviate the problem of outliers, this chapter aims to develop two different option pricing prediction strategies based mainly on the idea of robust linear regression. The robust techniques proposed are evaluated on numerical data, and the results demonstrate their effectiveness for pricing European call options on exchange rates.