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小蜜蜂jj1 · 2023年03月26日

-0.9的意思是什么？

  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。

就是long put和买asset吗？如果是正数就是sell call和买asset？

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2 个答案

Lucky_品职助教 · 2023年05月26日

嗨，爱思考的PZer你好：


回复 Ivana ：NP＝1是假设，这种题目的做题思路按照李老师讲的，就是首先计算出ns，根据正负判断long unit还是short unit，然后再判断期权的long和put。

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Lucky_品职助教 · 2023年03月29日

嗨，从没放弃的小努力你好：


就是long put和买asset吗？--是的。

如果是正数就是sell call和买asset？--正数的话是 short stock，那对应应该是long call

本题由NP=1推导出ns=0.9，由于得出为正数，所以是buy stock，为了构建hedged portfilio，我们还需要long put，因此组合起来就是long put long stock

这种题目的做题思路按照李老师讲的，就是首先计算出ns，根据正负判断long unit还是short unit，然后再判断期权的long和put。

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Ivana 🍭 · 2023年05月26日

老师请问NP＝1是假设的吗？long 还是short是看hp＞0还是＜0吗？

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