Bias Reduction in European Option Pricing

Pricing European options using price estimates of the underlying security that contain noise, create a bias in the option price. We present a technique to reduce this bias. Using ideas from the Longstaff and Schwartz (2001) algorithm, we prove that when the price of the underlying security belongs to a space spanned by a set of basis functions, the bias reduction technique can effectively remove the option price bias. In this setting we prove (i) the option price bias can be controlled by increasing the computational burden (ii) the proposed estimator for the price of the underlying security is less volatile than the crude Monte Carlo estimate and (iii) the resulting option price estimator is consistent. The technique is particular efficient when a lot of computational effort has to be allocated to reduce the option price bias.