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蜗牛也是牛Megan · 2025年05月05日

periodic fixed swap rates

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

1 个答案

李坏_品职助教 · 2025年05月05日

嗨,从没放弃的小努力你好:


不一定都是年化。如果题目问你annual swap rate,或者直接问annual fixed rate,那是年化。


这个题目问的是periodic fixed swap rate, 就是周期性的,每一个周期的swap rate。那就是每半年支付或收取的那个fixed rate,这个是不需要年化的。

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努力的时光都是限量版,加油!

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