NO.PZ2021061002000067
问题如下：
An asset manager owns non-dividend-paying
stock in XYZ Corporation, currently priced (S0) at $50 a share. The
asset manager is considering selling shares at a forward price (F0(T))
of $54 per share in six months at a risk-free rate of 2%.
Now consider buying a put option or selling
a call option with an exercise price (X) equal to the forward price (F0(T))
as an alternative to a forward stock sale.
Based on the above information, answer the question：
The asset manager is considering buying a put
option to hedge against a fall in XYZ's share price. Which of the following
statements is most accurate about the tradeoff between put options and forward
contracts under no-arbitrage pricing?
选项：
A.If the put option ends up in the money at
maturity, the gain on the forward sale will equal the purchased put option’s
profit at maturity.
Because we do not know the time value of
the option at maturity, we do not have enough information to answer this
question.
The loss on the forward sale will exceed
the loss on the purchased put at maturity if XYZ’s share price exceeds the
forward price by more than the initial put premium paid.
解释：
中文解析
为了对冲股价下跌的风险，题干中提到了short forward，long put，short call三种方法。
本小题中比较的是short forward和long put两种方法。
Short forward在合约到期的时候的收益为F0(T)-ST。
Long put的profit为max{0，X-ST}-p0.
其中F0(T)=X。
当到期时候ST高于F0(T)时，那么：F0(T)-ST
short forward的损失为：- p0
Long put的损失为：
且如果ST高于F0(T)的部分超过了p0的时候，意味着short forward的损失是更高的，C选项对。
NO.PZ2021061002000067的讲解感觉有点问题。这道题和time value有什么关系吗？time value不是计算option price用的吗？我们是不是应该只关注到期时的exercise value，以及解析中所说的p0？
