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alanmyl · 2023年03月01日

请问这道题如果用每期现金流折现思路计算可以吗,比如第二年收益是250*(8%-7.5)

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.

第三年是250*(8.5%-7.5)折现率用7.5%?

1 个答案

DD仔_品职助教 · 2023年03月01日

嗨,努力学习的PZer你好:


同学你好,

净值折现这个思路没有什么问题,但是你这个应该是第二年的net cf不应该用7.5%而是应该用当时的利率8.5%,第一年的net cf用8%折现。

思路对但不建议你这么做,因为我们课上讲了对于IRS,float的一方每次reset之后的value都是等于面值的。如果我们按照折现的公式去算的话,算出来浮动端的value应该略低于250,这样算出的答案会有出入。

做题的时候还是按照float的一方价值等于面值来算比较稳妥。

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