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比如世界 · 2020年05月27日

问一道题:NO.PZ2016082402000065

问题如下:

A bank entered into a three-year interest rate swap for a notional amount of USD 250 million, paying a fixed rate of 7.5% and receiving LIBOR annually. Just after the payment was made at the end of the first year, the continuously compounded spot one-year and two-year LIBOR rates are 8% and 8.5%, respectively. The value of the swap at that time is closest to

选项:

A.

USD 14 million

B.

USD -6 million

C.

USD -14 million

D.

USD 6 million

解释:

ANSWER: D

This question differs from the previous one, which gave the swap rate. Here, we have the spot rates for maturities of one and two years. The coupon is 7.5. The net present value (NPV) of the payments is then V=$18.75e1×8%+($250+$18.75)e2×8.5%=$244million.V=\$18.75e^{-1\times8\%}+{(\$250+\$18.75)}e^{-2\times8.5\%}=\$244million. Right after the reset, the value of the FRN is $250 million, leading to a gain of $6 million. This is a gain because the bank must pay a fixed rate but current rates are higher.

这题不是有libor吗 为什么不用单利计算固定端的价值呢(虽然题目浮动端的价值直接等于面值,也没有告诉具体的libor值,是不能用libor来计算的)

2 个答案

品职答疑小助手雍 · 2020年05月28日

1.折现不用连续复利的话可以用普通复利,比如1+8.5%的2次方这种,但是没有用1+8.5%*2这种单利折现的方式的。

2.不推荐利息差这种方式,因为libor作为spot rate其实并不完全等于swap rate,所以得到的答案会有细微的差异,还是建议用浮动债等于面值和固定债折现求现值的方式来算。

品职答疑小助手雍 · 2020年05月28日

嗨,努力学习的PZer你好:


没看明白单利计算固定端价值是什么意思

刚刚第一次互换后,也就是利率刚刚重置,那浮动端肯定是等于面值的。

而固定端,相当于给了折现率(8%和8.5%),已知了现金流(本金250,付息率7.5%),那现金流直接按照利率折现求债券价值就行了的。


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比如世界 · 2020年05月28日

1、折现的时候为什么不是用单利折现,而是用连续复利折现? 2、用每年末利息差(7.5%-8%)和(7.5%-8.5%)的折现值,这个思路对吗

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