NO.PZ2025040202000059
问题如下:
Question A company enters into a 2-year pay-fixed USD, receive-fixed EUR currency swap with semiannual resets. The spot interest rates and present value factors at initiation of the swap are as follows:
The respective EUR and USD periodic fixed swap rates are closest to:
选项:
A.A.1.22% and 1.93%. B.B.2.00% and 3.18%. C.C.2.44% and 3.86%.解释:
A Correct because
the EUR periodic fixed rate is calculated as rEUR
= [1 − PV2Y,EUR (1)]/[PV0.5Y,EUR (1) + PV1Y,EUR (1)
+ PV1.5Y,EUR (1) + PV2Y,EUR (1)]
= (1 − 0.952381)/(0.992556 + 0.982318 + 0.968054 + 0.952381) ≈ 1.22%.
The USD periodic fixed rate is calculated
as rUSD
= [1 − PV2Y,USD (1)]/[PV0.5Y,USD (1) + PV1Y,USD (1)
+ PV1.5Y,USD (1) + PV2Y,USD (1)]
= (1 − 0.925926)/(0.988631 + 0.971817 + 0.950997 + 0.925926) ≈ 1.93%.
B Incorrect because 2.00% and 3.18% refer
to the arithmetic average of the spot interest rates in each currency over the
four semi-annual periods, not the periodic fixed swap rates. They are
calculated as
(1.50% + 1.80% + 2.20% + 2.50%)/4 = 2.00%
for EUR rates and
(2.30% + 2.90% + 3.50% + 4.00%)/4 = 3.175%
≈ 3.18% for USD rates.
C Incorrect because 2.44% and 3.86% refer
to the respective EUR and USD annualized fixed swap rates, not the periodic
fixed swap rates. Annualized fixed swap rates are calculated as two times the
periodic fixed swap rates, i.e.,
2 × (1 − 0.952381)/(0.992556 + 0.982318 + 0.968054 + 0.952381) ≈ 2.44% for EUR rates and
2 × (1 − 0.925926)/(0.988631 + 0.971817 + 0.950997 + 0.925926) ≈ 3.86% for USD rates.
这个是什么概念,老师哪里讲过?不是求互换的都要年化吗