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PJ-John · 2021年04月13日

为什么1.2%可直接减0.8%

  1. CFA II
  2. Derivative

NO.PZ2019010402000015

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。

收固定 故5时刻向上流入金额为（1+1.2%*3/12）*100000000 然后用1.5%贴现

付浮动 故2时刻向下流出金额为100000000

这样算出来与结果为什么不符合？

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3 个答案

WallE_品职答疑助手 · 2021年05月04日

嗨，爱思考的PZer你好：


这道题不能用老李的画图法。下图中方法1为画图法，画图法的原理就是现金流折现再轧差，但是期末的现金流折现的时候要根据当前的市场libor折现，也就是按照0.8%折现，而这道题目明确要求是按照1.5%折现，所以不能按照第一种方法算。方法2为是期末做差在折现。


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WallE_品职答疑助手 · 2021年04月17日

嗨，爱思考的PZer你好：


因为您之前描述的是，

收固定 故5时刻向上流入金额为（1+1.2%*3/12）*100000000 然后用1.5%贴现

付浮动 故2时刻向下流出金额为100000000

这两个时间点对不上。



您看这才是答案折现的思路，如果您说用0.8%折现 那分子上减去的部分折现后就变成1了，所以才会恰巧一样。考试的话如果也像这样说吗了折现率那就得用它说的。

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Qqnd · 2021年05月04日

我也有同样的疑问，想用李老师的画图大法计算这道题，得到了和楼主相同的两项，相减得不出答案。可不可以请老师用这道题带入一下画图大法的公式？我记下的公式是 V = NP - NP (1 + FRA x tm ) / (1 + Lhm x tm) 所以 V = 100m - 100m ( 1 + 1.2%/4) / (1 + 1.5%/4) 是我哪个数字代错了嘛？

WallE_品职答疑助手 · 2021年04月14日

嗨，爱思考的PZer你好：


贷款开始日,也就是2时间点，相当于如果不签订合约，我的贷款利率是libor，签订合约后我的贷款利率是FRA约定的fix rate。因此我们在5时间点会用，所以这两笔轧差是发生在5时刻的，因此要在5时刻减去后再乘以本金然后在折现。

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