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Nicole Cai · 2024年08月19日

解题

NO.PZ2023040401000105

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:

A is correct.

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

得出h=-0.9怎么是选项A? 这题能不能解释下?

1 个答案

李坏_品职助教 · 2024年08月19日

嗨,爱思考的PZer你好:


本题问你,如何利用put option与stock,构造一个完美对冲组合?所谓完美对冲,意思是0时刻构造的组合,在期末无论股价涨跌,组合的价值都一样。


按照binomial model基础班讲义的内容:

这个h的公式是用call option进行完美对冲的条件,本题只需替换为put option即可,也就是h = (p1u - p1d) / (S1u - S1d) = -0.9.


buy put option,股价越跌越赚钱,股价越涨反而可能亏钱,为了对冲股价上涨的风险,需要再加上buy stock。而h的绝对值就是buy stock的数量(需要buy 0.9份stock)。所以A选项说的buy put + buy 0.9 stock是对的。


可以看看基础班Binomial Model这个章节的例题讲解。





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