问题如下图：
选项：
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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！
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!
$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?
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 ) )
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？
也就是6时刻的6个月libor，所以不用。