请教一个关于期权价格和内在价值的问题

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以无收益资产为例，看涨期权的执行时刻回报为max(s1-X,0)，当前期权价格是对整个回报max(s1-X,0)的贴现，先取较大值，再贴现；而当前期权的内在价值是对未来的(s1-X)先贴现再取最大值。这两者的差异正体现了期权多头权利义务的不对称性。 请问这句话该如何理解呢，他们两个得出来的结果是不一样的么？ 我觉得都一样啊？想不明白，请教   


S1是在未来某时刻标的资产的价格，X是执行价格

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关键词：内在价值 如何理解 max 不对称 不明白 价格 期权 价值

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,

Chemist_MZ 发表于 2013-5-21 07:47
I agree with tracytaop

Let me add something more.

强人！受益匪浅

Chemist_MZ 发表于 2013-5-21 07:47
I agree with tracytaop

Let me add something more.

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

BlademasterX 发表于 2014-10-29 23:01
excuse me sir, im really impressed by your comment though it's been a long time....i just dont com ...

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.

Chemist_MZ 发表于 2013-5-21 07:47
I agree with tracytaop

Let me add something more.

为老弟第一段精彩点评狂赞不止~
题外话，其实不单是学生，国内不少编书的教授都很容易忽视这个最基本的概念，那种直接对max折现的大有人在，当然还有他们的书在。
另外，你后面写的那个内在价值=max（discount（ST）-X，0）是不是有点问题，我怎么觉得应该丢掉折现因子？
请赐教，谢谢~