NO.PZ2020021205000066
问题如下:
what position should be taken in the two options and the underlying asset for delta, vega, and gamma neutrality?
解释:
If the position is Xa in option A and Xb in option B we require
400 + 2Xa + 3Xb =0
60+0.4Xa + 0.5Xb=0
The solution to these equations is Xa = 100, Xb = -200. The position taken should therefore be a long position of 100 in option A and a short position of 200 in option B. This creates a delta of: 0.8 X 100 + (-0.6) X (-200) = 200 It is therefore necessary to sell 200 of the asset to maintain a delta of zero.
老师好,关于这道题有几个问题:
1、先调gamma明白,但是vega也是一阶导,为什么要先调vega?为什么不先调gamma,再同时调vega和delta?
2、在听课的时候就有疑问,既然先调gamma,portfolio+期权的组合已经是0了,也就是不管delta怎么变,得塔期权的价值也不变了,为什么还要调delta?所以这里的第二条红线就不明白。
3、引入stock后gamma不变理解,因为股票的delta是1,常数的二阶导是0,但是为什么引入stock后vega也不会变化?
4、800+120怎么就等于200了呢?