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Yang · 2020年06月01日

问一道题：NO.PZ201903040100000106

  1. CFA II
  2. Derivative

* 问题详情，请 查看题干

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.

这道题为什么要用 90-day libor 和 180-day LIBOR 折现，而不用下面句子中提到的 1.1%？

 Johnson determines that the appropriate discount rate for the FRA settlement cash flows is 1.10%.

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WallE_品职答疑助手 · 2020年06月02日

因为题目要你求的是 The value of the 6 x 9 FRA 90 days after inception 是站在3时刻求估值，所以就用当前3时刻的6个月libor折现。

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NO.PZ201903040100000106 $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. 为什么这道题目不需要用到scout factor？能否画个图一下？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swvalue的区别在什么地方？两者的计算公式有怎么样的区别？谢谢！

2021-10-04 21:01 1 · 回答

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