On the use and improvement of Hull and White's control variate technique

A study of the use and improvement of Hull and White's (1988) control variate technique in pricing options is provided. It contributes to the literature in two ways. First it is shown that it is not optimal to use the entire error of a control variate against its known price (usually a closed-form solution) to correct and improve the unknown error of the unknown price of a complex option and a better error correction fraction is derived. Secondly, while Hull and White only advocated the use of the simplest European option control variate, it is shown how to choose better controls to reduce pricing errors more effectively and the role of so called static hedges as the best theoretical control variates is discussed.