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Annie彧 · 2023年07月29日

Negative delta results in short volatility position, 这句话怎么理解?

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NO.PZ202212300200003402

问题如下:

Kelly meets with Anusha Bandla, another high-net-worth client, who expects very little price movement in BKLN. Bandla evaluates the options strategies to take advantage of BKLN’s volatility and makes the following three statements:

Statement 1: For a 1% move in the options volatility, the value of an ATM straddle would change by $0.506.

Statement 2: A short volatility strategy can be established by implementing an ATM straddle.

Statement 3: To protect downside risk, a collar strategy can be implemented by adding a long put to a covered call position.

Which of Bandla’s statements is least likely correct?

选项:

A.

Statement 1

B.

Statement 2

C.

Statement 3

解释:

Statement 1 is incorrect

Vega of ATM options with a strike price of $510 is 0.320

Vega of straddle = 0.320 + 0.320 = 0.640

For a 1% move in the options volatility, the value of ATM straddle would change by $0.640.

Statement 2 is correct

ATM straddle = Call delta + Put delta = 0.506 + (– 0.514) = –0.008

Negative delta results in a short volatility position.

Statement 3 is correct

Collar = Protective put + Short call (OTM)

Collar = Covered call + Long put (OTM)

Covered call = Long stock + Short OTM call

Protective put = Long stock + Long put

Statement 2 可以解释一下为什么正确吗?

1 个答案

pzqa31 · 2023年07月30日

嗨,爱思考的PZer你好:


表述2想表达的意思是站在delta的角度,按照delta 小于0可以理解为是short option的思路,而short volatility strategy也可以理解为short option的意思,从而判断这个表述是正确的。


具体我们来分析一下:

(1)这里说short volatility strategy是short option的意思,是因为option的策略本身是一个volatility的策略,因为option赌的是股票价格的变动,option的而价格是和volatility有关系的,所以short volatility就是short option的意思。

(2)通过计算可知这个straddle的策略的delta是小于0的,即股票上涨一块钱,option的value是下降的,所以相当于一个short option的策略。

(3)结合上面两个思路,于是可以得到表述2是正确的。如果还有疑问,这道题是2021年的Mock题,同学可以去详细听一下讲解。

(4)注意这里计算一个strategy的delta小于0,然后把它当做一个short option的策略,即short volatility策略。这种判断方法反过来并不一定是成立的。如long put是long option的策略,但是delta是小于0的;同样也有成立的情况,如short call是short option的策略,他的delta就是小于0的。


所以我们这种通过delta的正负来判断一个策略(注意是option的组合策略)的long short 头寸,可以认为是以call为参考的,并不适用于广泛的option。

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