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kkyy · 2020年10月03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.

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 ) )

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1 个答案

xiaowan_品职助教 · 2020年10月04日

嗨，从没放弃的小努力你好：


同学你好，

这道题是今年经典题FRA这个视频里3.2题，我截一张老师板书的画图和计算式，你可以参考一下，根据你给的计算式，前半部分0.95%有误，该处应使用0.9%


-------------------------------
加油吧，让我们一起遇见更好的自己！


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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

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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

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2020-07-04 11:34 1 · 回答