Abstract
We consider a square-integrable semimartingale and investigate convex order relations between its discrete and its continuous realized variance. We show that under conditional independence of increments and for symmetric jump measure, discrete realized variance dominates quadratic variation in increasing convex order. The results have immediate applications to the pricing of options on realized variance. For a class of models including time-changed Lévy models and Sato processes with symmetric jumps our results show that options on variance are typically underpriced if quadratic variation is substituted for the discretely sampled realized variance.