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Zhj006 · 2025年04月13日

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NO.PZ202304100300001302

问题如下:

Based on Exhibit 6 and the three-month US dollar Libor at expiration, the pay­ment amount that the bank will receive to settle the 6 x 9 FRA is closest to:

选项:

A.

$19,945.

B.

$24,925.

C.

$39,781.

解释:

Given a three-month US dollar Libor of 1.10% at expiration, the settlement amount for the bank as the pay-fixed (receive-floating) party is calculated as

Settlement amount pay-fixed (receive floating)


Settlement amount pay-fixed (receive floating)

= $20,000,000[(0.011 - 0.0070)(90/360)]/[1 + 0.011(90/360)]

Settlement amount pay-fixed (receive floating) = $20,000/1.00275 = $19,945.15

Therefore, the bank will receive $19,945 (rounded) as the receive-floating party.

分子为什么不是1.011的(90/260)次方?

1 个答案

李坏_品职助教 · 2025年04月13日

嗨,爱思考的PZer你好:


FRA本身的期限 = 9-6 = 3个月,也就是90天。


而FRA rate以及Libor rate都是年化利率(对应的是360天),所以分子要进行“去年化”的处理(把360天的年化利率,转化为90天的实际利率),也就是(0.011 - 0.0070) * (90/360)。


分母应该是把期末t=9这个时刻的现金流折现到t=6的时刻(从t=9折现到t=6,那也是90天),因为FRA都是提前结算的,提前到t=6结算。并且FRA用的都是单利计算模式,所以分母必须是1+libor * (90/360)



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