老师，这道题哪里的信息提供的是before maturity？

问题如下：

A European put option with six months remaining to maturity has an exercise price (X) of USD 48. Suppose the underlying stock has no additional cash flows, the risk-free rate is 2%, the current underlying price (S_t ) is USD 54. If the current put option price is USD 4.6,

Which of the following calculations of the exercise value and the time value is correct?

选项：

A.

The exercise value of the put option is 0;The time value of the put option is USD 4.6.

B.

The exercise value of the put option is 4.6; The time value of the put option is USD 0.

C.

The exercise value of the put option is 0；The time value of the put option cannot be calculated.

解释：

中文解析

计算如下：

Put option exercise value = Max (0, X(1 + r)^−(T−t) − S_t) = Max(0, 48(1 + 2%)^−0.5 − 54) = 0

Put option time value = ​p_t – Max (0, X(1 + r)^−(T−t) − S_t) = 4.6-0 = USD 4.6