Using the continuous price as control variate for discretely monitored options

Variance reduction is of highest importance in financial simulation. In this study, we present a new and simple variance reduction technique for pricing discretely monitored lookback and barrier options. It is based on using the corresponding continuously monitored option as external control variate. To obtain the value of the continuously monitored price both, conditional simulation and conditional expectation can be utilized. From numerical experiments we can conclude that the efficiency gains obtained by our new method are significant.