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Roseline · 2020年11月17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.

老师好,想和您确认一下,这道题是因为要求在reset date的value,所以浮动端不需要考虑利息;而Financial Market and Product经典题无答案版本第68页的第2.1题,是因为要求在0时刻的value, 所以浮动端需要考虑利息。这么理解对吗?(经典题2.1题截图如下)


1 个答案
已采纳答案

品职答疑小助手雍 · 2020年11月17日

嗨,爱思考的PZer你好:


经典题也不算是t0时刻把,它说的是剩余15个月,也就是前面已经过了一段时间了,而且它半年互换一次的话,现在第一次付款期还有3个月,也就是说现在是reset date之后又过了3个月的情况,市场上的利率产生了变化。


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