Before revision: We consider a square-integrable semimartingale with conditionally independent increments and symmetric jump measure, and show that its discrete realized variance dominates its quadratic variation in increasing convex order.
After revision: We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, and show that its discrete realized variance dominates its quadratic variation in increasing convex order.