请教一道关于美式期权Delta的题

yufangping 发表于 2015-8-13 14:57
1.你分别比较一下任何时刻期权价值和如果执行得到的intrinsic value价值的大小就知道了，call的话在任意一 ...

correct

volbaseball 发表于 2015-8-14 08:13
非常感谢你的回答！
不过我还是不太明白，想再问一下，这个解释是仅仅针对这一题而言吗？因为这一题的Ca ...

你得把题目重新说一遍光这么说不是很清楚，例如call是ITM，delta就不可能是0.25

volbaseball 发表于 2015-8-14 08:13
非常感谢你的回答！
不过我还是不太明白，想再问一下，这个解释是仅仅针对这一题而言吗？因为这一题的Ca ...

我再稍微解释一下yufangping的回答，这样你可能可以自己回答你别的疑问。

美式的call只有没有dividend才不会提前被行权，期权的time value可以更细得划分成两个部分，一个是time value of money，第二个是期权带来的insurance value（因为期权相当于是买了一个保险）。这两部分有具体的表现形式，对于time value of money而言call是pay K得到股票，而put是sell股票得到K，因此对于call而言你更有倾向晚pay K（可以多得利息），而对于put你希望早得到K，多得利息。而对于insurance value来说两者都是时间越长不确定性越高，提供的保护价值就越大。因此你会发现对于call两者是一致的，我都倾向于越晚越好，而对于put，虽然我有保险价值，但是如果保险价值小于我损失的利息，我宁可早行权。因此put会有一个最优行权点，这个点就是time value of money和insurance value互相抵消即总的时间价值为0的时刻，这个显然取决于很多因素，例如利息，以及股票的波动率，到期时间等。

如果加入股息，call的analysis会有所变化，例如是离散的非连续的股息因为如果股票pay 了股息股价会下降，但是K不会跟着调整，因此call会贬值，因此最优策略是持有call到pay 股息的前一秒行权。对于连续的股息，一样的道理，股票会以qdt的速度下降，而利息会以rdt的速度上升，如果股息够大，你一定倾向于提前行权。put有类似的分析，你可以自己当做practice

Chemist_MZ 发表于 2015-8-14 11:11
我再稍微解释一下yufangping的回答，这样你可能可以自己回答你别的疑问。

美式的call只有没有dividend ...

收益颇丰！
不过我所理解的美式put可能提前行权的主要原因是股价下行空间有限所致，一旦股价足够低从而提前行权变现可能更为有利。另外，感觉时间价值往往是通过总价值与内在价值作差来间接量化的，不知道斑竹对时间价值的两个细分部分相互抵消的分析是如何量化的？谢谢。

chengzhifu2013 发表于 2015-8-30 10:46
收益颇丰！
不过我所理解的美式put可能提前行权的主要原因是股价下行空间有限所致，一旦股价 ...

You always compare waiting value Vs exercise value

Exercise value is straightforward while waiting is a little tricky because when you wait for something you always sacrifice something else. In this case, it is you want insurance value but with the cost of time value of money. What you said "更为有利“ "更“ is still a comparison. Why it can be "more"? Of course you are comparing with something else which is obviously WAITTING. So still time value of money (or more comprehensively, financing cost) and insurance value come into play. The explanation with my theory is because deep in the money put option does not have much insurance value from the volatility. It is almost the same as shorting a forward (The delta is close to -1) which does not have value contributed by vol.

There is no need to quantify, because you know there is a point when this can happen. Just like the proof of solution existence in math.  To quantify the value, I think there is a naive way to do this. Firstly find the point where European put option has zero time value. Then change r=0 and see what is the time value (x) because that would mean all the time value is contributed by the volatility. Then the time value contributed by financial cost should be -x. Or we can do in a reverse way set vol=0 (or a very small number because BS does not allow vol=0) then the time value would all come from interest rate. Hopefully this will work. Again, this way of decomposition is proposed by myself. There might be some problem inside. It is a good way of thinking to explain some common options questions. To quantify, we may need more work.

Chemist_MZ 发表于 2015-8-30 11:51
You always compare waiting value Vs exercise value

Exercise value is straightforward while wait ...

“Then change r=0 and see what is the time value (x) because that would mean all the time value is contributed by the volatility. Then the time value contributed by financial cost should be -x. Or we can do in a reverse way set vol=0 (or a very small number because BS does not allow vol=0) then the time value would all come from interest rate. ”
十分感谢详尽的解答，仍有稍许困惑：
当令vol为一个很小的值时，vol与r已经不满足正交条件了还可以这样单独地分析这两者对时间价值的影响吗？

chengzhifu2013 发表于 2015-8-31 10:04
“Then change r=0 and see what is the time value (x) because that would mean all the time value is ...

if they have correlation then of course not, you need to decompose further such as financial cost, insurance value and cross correlation risk. But I have not seen a model model r's correlation with vol, of course exclude interest rate options in our discussion. Low vol does not mean any correlation. Can you elaborate your question?

Chemist_MZ 发表于 2015-8-31 10:37
if they have correlation then of course not, you need to decompose further such as financial cost, ...

我的意思是，r和vol对于时间价值的影响可能存在协同效应。一般地，r与证券价格（包括股价）之间存在反向关系，那么这种反向关系是否还会受到来自vol的影响呢？如果是，则显然就存在所谓的协同效应。

chengzhifu2013 发表于 2015-9-1 14:56
我的意思是，r和vol对于时间价值的影响可能存在协同效应。一般地，r与证券价格（包括股价）之间存在反向关 ...

still don't understand. Can you give an example? A and B both have impact on C but you can not say A and B are correlated. I don't think r has correlation with vol. You can not say r has correlation with price and price has correlation with vol so that r has correlation with vol.

Chemist_MZ 发表于 2015-8-13 07:57
美式put没有公认的解析解，大家都在试图寻找。所以美式put的delta没有精确的公式。虽然判断不了绝对的值，但 ...

你不是算出来delta_P>-0.75吗？不应该是大于-0.75？