期权的价格受各种因素影响，从理论上来说，由两个部分组成，内在价值和时间价值。对于你问题中的这句话：“价格是先取最大值，再贴现，而内在价值是先贴现，再取最大值”，当期权是虚值期权或者平价期权时，此时内在价值是等于零的，而价格是不可能为零，必会以大于零的价格成交。因为看涨期权中，如果市场价格低于协定价格，就是虚值期权，此时期权的内在价值是负的，那么买方就可以选择放弃期权，这是他的权利。而他为了获得这种权利，从一开始就需要支付额外费用。所以说，内在价值可能为零，而价格是不可能为零的。买方就是所谓的多头是有权利而没有义务（他的义务就是开始的时候支付价格）而卖方就是空头，是有义务而没有权利，多头的权利义务不对称，就是这个意思。

I agree with tracytaop

Let me add something more.

The price of the call option is not just discount max(ST-X,0) but the "expectation" of max(ST-X,0). Say you are now at time t you will not know ST until you arrive at T. You actually average the payoff by taking expectation to consider all the possibilities. This solves your confusion that you think there is no difference between these two statements.

The intrinsic value of the option totally depends on time t. That is max(St-X,0) not capital T. Of course St can be regarded as discounted ST. In this case, the statements make sense.

You see the difference? If we write in an informal way:

call option price=discount(E(max(ST-X,0))
intrinsic value=max(discount(ST)-X,0)

Option gives you the right to choose depending on the unknown future ST. So you have to pay something for this right. Intrinsic value can be regarded as something as the "known" part of the option's value. The difference of the option's total value and the "known" value is the "unknown" part which reflects the uncertainty's value.

Of course, the fundamental reflection of the asymmetrical right and obligation lies in "max" not in the difference of the option's price and the intrinsic value. So, I think this statement is not orgnized in a very strict way. Asymmetrical right and obligation gives you the intrinsic value and the uncertainty give you the time value. In total, they are the option's value.

best,

强人！受益匪浅

excuse me sir, im really impressed by your comment though it's been a long time....i just dont comprehend why the 'discount' is placed differently. I mean, what do they refer respectively? could you please go into little bit details about it?
many thx

It is because the question is asking about it. Again, this is an informal way of expression. I really don't want to write in this way. And the original question does not even make sense to me. So you can totally ignore my comment.