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Jack Sun · 2021年10月04日

FRA value vs swap value

  1. CFA II
  2. Derivative

* 问题详情，请 查看题干

NO.PZ201903040100000106

问题如下：

6.From the bank’s perspective, based on Exhibits 6 and 7, the value of the 6 x 9 FRA 90 days after inception is closest to:

选项：

A.

$14,817.

B.

$19,647.

C.

$29,635.

解释：

A is correct. The current value of the 6 x 9 FRA is calculated as

Vg(0,h,m) = {[FRA(g,h - g,m) - FRA(0,h,m)]tm}/[1 + Dg(h + m - g)th+m-g]

The 6 x 9 FRA expires six months after initiation. The bank entered into the FRA 90 days ago; thus, the FRA will expire in 90 days. To value the FRA, the first step is to compute the new FRA rate, which is the rate on Day 90 of an FRA that expires in 90 days in which the underlying is the 90-day Libor, or FRA(90,90,90):

FRA(g,h - g,m) = {[1 + Lg(h - g + m)th-g+m]/[1 + L0(h - g)th-g] - 1}/tm

FRA(90,90,90) = {[1 + L90(180 - 90 + 90)(180/360)]/[1 + L90(180 - 90) (90/360)] - 1}/(90/360)

FRA(90,90,90) = {[1 + L90(180)(180/360)]/[1 + L90(90)(90/360)] - 1}/ (90/360)

Exhibit 7 indicates that L90(180) = 0.95% and L90(90) = 0.90%, so

FRA(90,90,90) = {[1 + 0.0095(180/360)]/[1 + 0.0090(90/360)] - 1}/(90/360)

FRA(90,90,90) = [(1.00475/1.00225) - 1](4) = 0.009978, or 0.9978%

Therefore, given the FRA rate at initiation of 0.70% and notional principal of $20 million from Exhibit 1, the current value of the forward contract is calculated as

Vg(0,h,m) = V90(0,180,90)

V90(0,180,90) = $20,000,000[(0.009978 - 0.0070)(90/360)]/[1 + 0.0095(180/360)].

V90(0,180,90) = $14,887.75/1.00475 = $14,817.37.

为什么这道题目不需要用到discout factor？能否画个图解释一下？ 作为对比,书上同一个case的第9题的公式: 利率差*本金*折现因子之和。第9题考点为“求swap的fair value”。 我有点概念不清：FRA value和swap value的区别在什么地方？两者的计算公式有怎么样的区别？谢谢！
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1 个答案

WallE_品职答疑助手 · 2021年10月05日

嗨，爱思考的PZer你好：


这道题强调要用表6和表7，本身就没有给出discount factor.


FRA和swap是2种不同的产品，如果同学还不清楚，建议同学一定得在把课听一遍，这说明同学还是不清楚衍生品这门课在讲什么，这是一个很严肃的问题。


求value 笼统的说没有什么区别，全部都是未来现金流折现，不同的点在于用什么利率来折现，以及折现到哪个时候。这些都要依据题目给的信息来判断。

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NO.PZ201903040100000106 签合约时，t=0；now是t=3 和前面一个问题相对比（另一道题目为NO.PZ2019010402000013），下图30天libor、60天libor、90天libor、120天libor、150天libor、180天libor、210天libor、270天libor的数字，是对于t=3时点，还是t=0时点？ 另外，考试的时候也默认是在 t=（前面回答的时点），对吗？应该怎么判别?谢谢!

2021-10-04 01:37 1 · 回答

$19,647. $29,635. A is correct. The current value of the 6 x 9 FRA is calculateVg(0,h,m) = {[FRA(g,h - g,m) - FRA(0,h,m)]tm}/[1 + (h + m - g)th+m-g] The 6 x 9 FRA expires six months after initiation. The bank entereinto the FRA 90 ys ago; thus, the FRA will expire in 90 ys. To value the FRthe first step is to compute the new FRA rate, whiis the rate on y 90 of FRA thexpires in 90 ys in whithe unrlying is the 90-y Libor, or FRA(90,90,90): FRA(g,h - g,m) = {[1 + Lg(h - g + m)th-g+m]/[1 + L0(h - g)th-g] - 1}/tm FRA(90,90,90) = {[1 + L90(180 - 90 + 90)(180/360)]/[1 + L90(180 - 90) (90/360)] - 1}/(90/360) FRA(90,90,90) = {[1 + L90(180)(180/360)]/[1 + L90(90)(90/360)] - 1}/ (90/360) Exhibit 7 incates thL90(180) = 0.95% anL90(90) = 0.90%, so FRA(90,90,90) = {[1 + 0.0095(180/360)]/[1 + 0.0090(90/360)] - 1}/(90/360) FRA(90,90,90) = [(1.00475/1.00225) - 1](4) = 0.009978, or 0.9978% Therefore, given the FRA rate initiation of 0.70% annotionprincipof $20 million from Exhibit 1, the current value of the forwarcontrais calculateVg(0,h,m) = V90(0,180,90) V90(0,180,90) = $20,000,000[(0.009978 - 0.0070)(90/360)]/[1 + 0.0095(180/360)]. V90(0,180,90) = $14,887.75/1.00475 = $14,817.37. Inception如何理解?

2020-10-23 13:41 3 · 回答

能不能用直接求value的方式给我们画个图呢？我的算法，跟答案有些出入 我是NP*( ( 1/ ( 1+ 0.95%*60*360)) - ( 1+ 0.7%*90/360 / 1+0.95%*180/360 ) )

2020-10-03 13:55 1 · 回答

我按照FRA的原理，把支付固定利息的的三个月期贷款终值，用3个月的折现率1.1%，得到固定利息方向现金流的现值，与浮动方向现金流现值NP做差，然后用90天libor折现到当前。 1、6×9FRA在6个月时刻到期，进入3个月的贷款期，贷款终值为20,000,000×（1+0.7%×1/4); 2、将上述贷款终值用1.1%的折现率折现到贷款开始时，为20,000,000×（1+0.7%×1/4)/(1+1.1%×1/4） 3、用浮动利率在贷款开始时的现值20,000,000与上述固定利息贷款现金流现值做差，20,000,000-20,000,000×（1+0.7%×1/4)/(1+1.1%×1/4）=19,945.15 4、将上述结果用3个月libor0.9%折现到当前时刻，为19,945.15/(1+0.9%×1/4）=19,900.37. 请问这种算法错在哪里？为什么答案解析中不用1.1%的折现率？

2020-07-04 11:34 1 · 回答