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Kael · 2020年10月30日

问一道题：NO.PZ2019010402000015 [ CFA II ]

  1. CFA II
  2. Derivative

问题如下：

The company enters into a $100,000,000 notional amount 2 × 5 receive-fixed FRA that is advanced set, advanced settled. The appropriate discount rate for the FRA settlement cash flows is 1.5%. After 60 days, 90-day Libor is 0.80%, 60-day Libor is 0.7%.

If the FRA was initially priced at 1.20%, the payment received to settle the 2 × 5 FRA will be:

选项：

A.

100,000

B.

99,626

C.

99,800

解释：

B is correct.

考点：FRA settlement

解析：

payment received=(1.2%−0.8%)×312×100,000,0001+1.50%×312=99,626.4payment\text{ }received=\frac{(1.2\%-0.8\%)\times\frac3{12}\times100,000,000}{1+1.50\%\times\frac3{12}}=99,626.4

注：题目中特别说明了折现率是1.5%，所以直接用1.5%折现，不用90天的LIBOR折现。

老师您好，请问这个给定的折现率不应该说的是刚进入FRA合约的时候未来现金流的折现率么？因为FRA是advanced settled，现金流只可能发生在两个月后。当我们选择60天后的折现率的时候，这个给定的折现率为什么不能是一个迷惑项呢？毕竟60天后已经没有未来现金流了因为这一天就是settle day。我的理解是这一题在考察正确的折现率的选择的时候同时考差了advanced settled的现金流发生时间。
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1 个答案

xiaowan_品职助教 · 2020年10月30日

嗨，爱思考的PZer你好：


同学你好，

FRA确实是提前settle的，但是我们还是要计算一下提前结算的金额，在2时刻实际结算的金额并不是直接就为（1.2%-0.8%）*1million*3/12这么多，因为我们签FRA想要产生的效果是这个锁定loan的成本，所以（1.2%-0.8%）*1million*3/12是要在loan结束的时候体现出来的，我们在2时刻只是提前得到这部分钱，所以要折现，去掉2到5之间的时间价值。

这个折现率是需要我们做选择的，如果题目中不提到要用1.5%，我们就需要用0.8%作为折现率，题目中给了，我们就用1.5%。


-------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！


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