完全看不懂题目和选项在说什么🫠，麻烦老师翻译一下，还有每个选项都在说啥🫠

问题如下：

In evaluating the purchased put strategy (with X = F₀(T)), the CIO has asked you to consider selling the put in three months' time if its price appreciates over that period. Which of the following best characterizes the no-arbitrage put price at that time?

选项：

A.As VFO will exercise only if the spot price is below the exercise price, the lower bound of the put price is the greater of zero and the present value of the spot price minus the exercise price.

B.As VFO will exercise only if the spot price is below the exercise price, the upper bound of the put price equals the present value of the exercise price minus the spot price.

C.The put price can be no greater than the forward price and no less than the greater of zero and the present value of the exercise price minus the spot price.

解释：

C is correct.

The put exercise price, X (equal to F₀(T) in this case), represents the upper bound on the put value, while the lower bound is the greater of the present value of the exercise price minus the spot price and zero:

Max(0, X(1 + r)^−(T−t) − S_t) < p_t ≤ X$\text{Max}\left(0,X{\left(1+r\right)}^{-\left(T-t\right)}-S_t\right)<p_t\le X$

A is incorrect, as the lower bound of the put price is the greater of zero and the present value of the exercise price minus the spot price, not the present value of the spot price minus the exercise price.

B is incorrect, as the lower, not the upper, bound of the put price equals the present value of the exercise price minus the spot price.

中文解析

本题考察的是put option的无套利的价格范围：Max (0, X(1 + r)^−(T−t) − S_t) < p_t ≤ X

其中：p_{t,Lower bound} = Max(0, X(1 + r)^−(T−t) − S_t)；p_{t,Upper bound} = X

在本题中F₀(T)=X，因此本题选择C。