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blade8932 · 2023年01月03日

老师，H=-0.9也是模模糊糊算出来的，如果这道题是CALL呢

  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。

不知道前面到底应该BUY OPTION 还是SELL OPTION，后面是 buy units还是 sell unit

麻烦老师集中情况能系统的讲解下吗？谢谢！

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1 个答案

Lucky_品职助教 · 2023年01月06日

嗨，从没放弃的小努力你好：


如果是call

S1u = 50 * (1+10%) = 55, c1u=Max(0, 55-54)= 1

S1d = 50 * (1-10%) = 45, c1d=Max(0, 45 -54)= -9

h = c1u - c1d / S1u - S1d = (1+9) / (55-45) = 1

本题市场价格低于行权价，且股价在未来波动中，处于in the money的概率更大（只有价格大于54才会out of the money），因此买看跌赚的概率更大，其次我们可以从图像中判断应该long stock，这样在股价下跌的时候，可以很好的对冲风险

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