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v · 2021年09月05日

For vega neutrality, we can take a position of -200 in option A?

NO.PZ2020021205000044

问题如下:

From the information in the following table, estimate (a) what position should be taken in option A and the underlying asset for vega and delta neutrality, and (b) what position should be taken in option B and the underlying asset for gamma and delta neutrality. Note: when answering part (b) do not assume that the position in part (a) has been taken.

选项:

解释:

For vega neutrality, we can take a position of -200 in option A. This will create a delta of 0.8 X (-200) = -160, and 160 of the underlying asset should be purchased. For gamma neutrality, we can take a position of -120 in option B. This will create a delta of -0.6 X (-120) = 72, and 72 of the underlying asset should be sold.

请问这个200是怎么来的?


For gamma neutrality, we can take a position of -120 in option B. ,请问120是怎么来的?

1 个答案

DD仔_品职助教 · 2021年09月05日

嗨,努力学习的PZer你好:


同学你好~

首先,我们默认的是underlying asset的delta是1,gamma是0,这是结论,不需要额外给条件,应当直接作为已知条件来用。

a问,想要利用option A来使得underlying asset的vega和delta neutral。先对冲Vega,目前Vega=400,optionA的Vega=2,所以要short 400/2=200份A。此操作之后,会使得组合原来的delta变成-200份*0.8=-160,所以需要再long 160份asset使得组合的delta=0.

b问,想要利用B option使得underlying asset的gamma和delta neutral。先对冲gamma,gamma目前=60,option B的gamma=0.5,所以要short60/0.5=120份B,此操作会使得组合原来的delta变为-120*-0.6=72,所以要再short72份B来使得delta为0.

做此类题的方法都是先搞定Vega或gamma,然后再调delta~

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