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!