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临江仙 · 2023年02月02日

h=-0.9

  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。

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。


既然h=-0.9，那么short stock和short put也是OK的吧。

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Lucky_品职助教 · 2023年02月06日

嗨，努力学习的PZer你好：


本题中没有short stock和short put的选项哦

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努力的时光都是限量版，加油！

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