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李羊羊羊羊 · 2023年11月28日

为什么不选C

  1. CFA I
  2. Derivative

NO.PZ2021061002000071

问题如下：

Suppose the current price (S0) of a non-dividend-paying stock is $50, and a put option on the stock has an exercise price (X) of $54 with six months left to maturity. Now an investor believes that the stock’s price in six months’ time will be either 10% higher or 10% lower.

Which of the following is true about constructing a perfectly hedged portfolio using put options and their underlying stocks?

选项：

A.

Buy one put option and buy 0.9 units of the underlying asset.

B.

Buy one put option and sell 0.9 units of the underlying asset.

C.

Sell one put option and buy 0.9 units of the underlying asset.

解释：

解析：

S1u = 50 * (1+10%) = 55, p1u=Max(0, 54 -55)= 0

S1d = 50 * (1-10%) = 45, p1d=Max(0, 54 -45)= 9

h = p1u - p1d / S1u - S1d = (0-9) / (55-45) = -0.9

注意计算的h是每份期权对应的标的资产的份数。Long stock与long put构成对冲组合，因此A对。

不知道怎么区别buy和sell，计算出来是-0·9

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1 个答案

pzqa35 · 2023年11月30日

嗨，努力学习的PZer你好：


首先对冲的目的就是为了在underlying价格变动的情况下，portfolio的价格是不发生变化的。A选项买入看跌期权同时买入股票，构成了protective put组合，如果股票价格下跌，那么看跌期权会升值，如果股价上升，看跌期权价值会下跌，因此可以做到对冲的作用。对于C选项，卖出看跌期权买入股票，如果股价下跌，股票头寸亏钱，卖出看跌期权头寸也亏钱，就会造成损失加倍。

其次，这个h是对冲比率，在二级我们也会学到它就是delta，代表股价变动一单位，会造成option的价格变动幅度。对于看跌期权来看，它的delta是-1到0之间的，本身就是负数，所以这边判断hedge的构成buy还是sell还是得从价格波动造成股票头寸和期权头寸的变动情况来看。如果这道题从这个角度来看，其实我们不用计算也可以选出A的。

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