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hbc0728 · 2020年03月26日

问一道题：NO.PZ2016082406000048

  1. FRM II
  2. Credit Risk Measurement And Management

问题如下：

Assume that a bank enters into a USD 100 million, four-year annual-pay interest rate swap, where the bank receives 6% fixed against 12-month LIBOR. Which of the following numbers best approximates the current exposure at the end of year 1 if the swap rate declines 125 basis points over the year?

选项：

A.

USD 3,420,069

B.

USD 4,458,300

C.

USD 3,341,265

D.

USD 4,331,382

解释：

ANSWER: A

The value of the fixed-rate bond is   6(1+4.75%)1+ 6(1+4.75%)2+106(1+4.75%)3=103.420\;\frac6{{(1+4.75\%)}^1}+\text{ }\frac6{{(1+4.75\%)}^2}+\frac{106}{{(1+4.75\%)}^3}=103.420. Subtracting $100 for the floating leg gives an exposure of $3.4 million. More intuitively, the sum of the coupon difference is 3 times (6%−4.75%)$100=$1.25{(6\%-4.75\%)}\$100=\$1.25, or around $3.75 million without discounting.

请问为什么是分子用6%，而分母用4.75%，为什么不是用6%折现，谢谢！

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小刘_品职助教 · 2020年03月27日

同学你好，

做swap的value题目首先要明确下swap的现金流是什么形式，这道题里面进入的是一个 receive fix的swap，在期初签订之后，每一期 receive的利息都是固定的6%；这就是分子是6%的原因；在计算value的时候折现需要按市场（最新）收益率计算，按照题目中已知的条件，就是6%-1.25%=4.75%，所以折现用的4.75%，也就是你看到的分母。

实际上这道题中The value of the fixed-rate bond 可以直接按计算器得到 N=3 I/Y=4.75 PMT=6 FV=100。然后求PV=103.4201

朵朵0927 · 2020年07月27日

没看懂老师，为什么n=3?

小刘_品职助教 · 2020年07月27日

同学你好，

因为现在的时间点是at the end of year 1，这个swap是4年的，现在是第1年年末，所以还有3期，N =3。

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NO.PZ2016082406000048 Assume tha bank enters into a US100 million, four-yeannual-pinterest rate swap, where the bank receives 6% fixeagainst 12-month LIBOR. Whiof the following numbers best approximates the current exposure the enof ye1 if the swrate clines 125 basis points over the year? US3,420,069 US4,458,300 US3,341,265 US4,331,382 ANSWER: A The value of the fixerate bonis   6(1+4.75%)1+ 6(1+4.75%)2+106(1+4.75%)3=103.420\;\frac6{{(1+4.75\%)}^1}+\text{ }\frac6{{(1+4.75\%)}^2}+\frac{106}{{(1+4.75\%)}^3}=103.420(1+4.75%)16​+ (1+4.75%)26​+(1+4.75%)3106​=103.420. Subtracting $100 for the floating leg gives exposure of $3.4 million. More intuitively, the sum of the coupon fferenis 3 times (6%−4.75%)$100=$1.25{(6\%-4.75\%)}\$100=\$1.25(6%−4.75%)$100=$1.25, or aroun$3.75 million without scounting. More intuitively, the sum of the coupon fferenis 3 times {(6%-4.75%)}\$100=$1.25 (6%−4.75%)$100=$1.25, or aroun$3.75 million without scounting.

2021-03-29 23:09 2 · 回答

Assume tha bank enters into a US100 million, four-yeannual-pinterest rate swap, where the bank receives 6% fixeagainst 12-month LIBOR. Whiof the following numbers best approximates the current exposure the enof ye1 if the swrate clines 125 basis points over the year? US3,420,069 US4,458,300 US3,341,265 US4,331,382 ANSWER: A The value of the fixerate bonis   6(1+4.75%)1+ 6(1+4.75%)2+106(1+4.75%)3=103.420\;\frac6{{(1+4.75\%)}^1}+\text{ }\frac6{{(1+4.75\%)}^2}+\frac{106}{{(1+4.75\%)}^3}=103.420(1+4.75%)16​+ (1+4.75%)26​+(1+4.75%)3106​=103.420. Subtracting $100 for the floating leg gives exposure of $3.4 million. More intuitively, the sum of the coupon fferenis 3 times (6%−4.75%)$100=$1.25{(6\%-4.75\%)}\$100=\$1.25(6%−4.75%)$100=$1.25, or aroun$3.75 million without scounting. 请问为什么是分子用6%，而分母用4.75%，为什么不是用6%折现，谢谢！

2020-03-26 21:49 1 · 回答

Assume tha bank enters into a US100 million, four-yeannual-pinterest rate swap, where the bank receives 6% fixeagainst 12-month LIBOR. Whiof the following numbers best approximates the current exposure the enof ye1 if the swrate clines 125 basis points over the year? US3,420,069 US4,458,300 US3,341,265 US4,331,382 ANSWER: A The value of the fixerate bonis   6(1+4.75%)1+ 6(1+4.75%)2+106(1+4.75%)3=103.420\;\frac6{{(1+4.75\%)}^1}+\text{ }\frac6{{(1+4.75\%)}^2}+\frac{106}{{(1+4.75\%)}^3}=103.420(1+4.75%)16​+ (1+4.75%)26​+(1+4.75%)3106​=103.420. Subtracting $100 for the floating leg gives exposure of $3.4 million. More intuitively, the sum of the coupon fferenis 3 times (6%−4.75%)$100=$1.25{(6\%-4.75\%)}\$100=\$1.25(6%−4.75%)$100=$1.25, or aroun$3.75 million without scounting. 老师，没看出来什么意思？

2020-03-10 02:47 1 · 回答

老师，题目里不是4年合约，为啥答案只算三年？

2019-10-27 18:48 1 · 回答