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JK_MMMM · 2023年06月09日

请问用讲义上的公式算出来PD(派)是个负数 如图。

NO.PZ2020033002000034

问题如下:

Grapefruit Bank issued two semi-annual interest-bearing credit bonds, of which bond A matures after half a year, the coupon rate is 8.5%, the current price is $ 98, and the corresponding half-year T-bill interest rate is 4.5%. The bond B expires after one year, the coupon rate is 10%, the current price is $ 101, and the corresponding one-year T-bill rate is 5%. Assuming that their recovery rates are all 40%, and they will only default on the coupon payment date, which of the following statements is correct?

选项:

A.

The market implied risk-neutral default probability in the first half of the year is higher than that in the second half.

B.The market implied risk-neutral default probability in the first half of the year is lower than that in the second half.

C.The market implied risk-neutral default probability is equal in the first half and the second half.

D.

The market implied risk-neutral default probability in the first half and the second half cannot be compared.

解释:

A is correct.

考点:Spread Risk-DVCS and Credit Spread Curve

解析:对于bondA,通过金融计算器:PV=-98 FV=100 PMT=4.25 N=1 CPT I/Y=6.3776 年化YTM=12.76%spread=YTM-rf=12.76%-4.5%=8.255%债券B:PV=-101 FV=100 PMT=5 N=2 CPT I/Y=4.466% 年化YTM=8.93%spread=YTM-rf=8.93%-5%=3.93%根据题目已知RR=40%,那么spread=PD*RR,谁的spread大,PD肯定就大,A这个半年期bond的PD大于B这个一年期的bond,那么前半年的PD也就肯定大于后半年的PD



2 个答案

DD仔_品职助教 · 2023年06月09日

嗨,爱思考的PZer你好:


就像解析里写的,对于bondA,通过金融计算器:PV=-98 FV=100 PMT=4.25 N=1 CPT I/Y=6.3776 年化YTM=12.76%

spread=YTM-rf=12.76%-4.5%=8.255%

债券B:PV=-101 FV=100 PMT=5 N=2 CPT I/Y=4.466% 年化YTM=8.93%

spread=YTM-rf=8.93%-5%=3.93%

根据题目已知RR=40%,那么spread=PD*RR,谁的spread大,PD肯定就大,A这个半年期bond的PD大于B这个一年期的bond,那么前半年的PD也就肯定大于后半年的PD

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

DD仔_品职助教 · 2023年06月09日

嗨,爱思考的PZer你好:


同学你好,

你没有考虑这个债券的coupon,半年就会付息一次。所以偿还的不仅仅是100块,还会有半年一次的coupon。

像这种有coupon的类型,不建议用这种expected value的方法来计算,因为麻烦的很,容易出错,这种题型,建议同学直接用简化的近似的公式:YTM-rf=spread=risk-neutral PD*LGD=risk-neutral PD*(1-RR)

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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