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Amy_ywh · 2023年04月17日

简单一些的解题思路

NO.PZ2021061002000063

问题如下:

A client owns 1,000 common non-dividend-paying shares of K company, at a spot price of AUD124 per share. The client enters into a forward commitment to sell all the position in three months at a price of AUD 128.4.

Which of the following market events is most likely to result in the greatest loss in the forward contract MTM value from the client’s perspective?

选项:

A.

The rise in the risk-free interest rate.

B.

A fall in the risk-free interest rate.

C.

An immediate decline in the VIVU spot price following contract inception.

解释:

中文解析:

根据题干可知,客户想要通过远期合约在3个月后减少持有的股票头寸,因此他应该进入的是short forward头寸。

Short forward头寸下,MTM value = F0(T)/(1+r)T-t - St

由上式可以看到:无风险利率上涨会使得MTM value下降,也就是会产生loss。因此选A

而股票价格下跌,以及无风险利率的下跌会使得MTM value增加。

这道题,我可以不可以理解为,因为他已经订好了未来卖掉股票时候的价格。三年以后如果rf增加的话,这个股票价格也会提高,对于已经提前订好卖出价格的卖家来说就算是亏损?

1 个答案

Lucky_品职助教 · 2023年04月18日

嗨,从没放弃的小努力你好:


你这么理解也可以,但无风险利率影响的其实是衍生品的价格,而不是现货的价格,所以不是很严谨,最好可以按照我们MTM value的方式来解题:

由于该客户持有的是远期合约的short position(卖出头寸),因此他的MTM value可以表示为:F0(T)/(1+r)^(T-t) - St,其中F0(T)是合约到期日的远期价格,St是持仓时刻的标的物价格, r是无风险利率,T是合约到期日,t是当前时间。由此可见,如果无风险利率上涨,那么(1+r)^(T-t)会增加,从而导致MTM value下降,因此该客户将会产生loss。

相反,如果无风险利率下跌,那么(1+r)^(T-t)会减小,从而导致MTM value增加,从而该客户将会获得更多的收益。同时,如果标的物价格下跌,也会导致MTM value减小,但是由于该远期合约已经确定了未来出售价格,因此标的物价格的下跌不会对该客户造成更多的损失。

总之,该客户通过进入short forward position锁定了未来的卖出价格,因此无论标的物价格如何波动,他的损失或收益都取决于无风险利率的变化。

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