解题

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.

S₁^u = 50 * (1+10%) = 55, p₁^u=Max (0, 54 -55) = 0

S₁^d = 50 * (1-10%) = 45, p₁^d=Max (0, 54 -45) = 9

h = p₁^u - p₁^d / S₁^u - S₁^d = (0-9) / (55-45) = -0.9