For option pricing , dicounted option price process is martingale, but for future, future price process( do not discount) is a martingale. why? I think most of us get the answer in mind.

If the price of the asset is correlated with the interest rates, it depends on the numeraire. If one uses the money market account (fictitious account in which collects the overnight rate r each day), futures are Martingales but forward prices and European options generally have drift terms. If one uses a zero coupon bond (with maturity equal to the payment date of the future or option) then the forward price and European options are Martingales, but the futures have a drift term.Since interest rates are correlated with other interest rates, on swap desks, Eurodollar futures have a drift relative to forward rates; either the Eurodollar futures are Martingales (if discounting by the short rate) and the forward rates drift, or the the future rates drift and the forward rate is a Martingale (if discounting by a zero coupon bond or annuity). Either way, the difference is the Eurodollar convexity correction ... see Galen & Burke's account in an ancient Dean Witter report