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Jack Sun · 2021年10月04日

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  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.

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!



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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：


Exhibit 7 current libor.


和上题一样“current”是现在的意思

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

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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

$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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2020-10-03 13:55 1 · 回答

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2020-07-04 11:34 1 · 回答