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临江仙 · 2020年03月21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.

为什么浮息债在这里的面值是250?

之前老师讲t时刻求value的时候,是将浮息债的利息+本金一起折现的。

为什么老师的方法,在这里不适用,求指导

1 个答案
已采纳答案

品职答疑小助手雍 · 2020年03月21日

同学你好,利率互换的固定端和浮动端的本金是一样的,所以浮动端也是250。

刚过付息日的时候,浮动端是不需要计算价值的,因为刚过付息日的时候浮动端的价值就等于面值。

以上两点都是课上讲过的定义和结论,而且很重要。

你说的t时刻那个不是刚过付息日这个节点。课上讲那个其实是隐含了一种假设,就是从付息日刚过到t时刻这两个时间点,利率曲线发生了变化。是更复杂的情况。

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