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小爽加油呀 · 2023年09月07日

N为什么不用0.5和1

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

为啥用1和2,用0。5算出来是i/y=8.7610,这个是不是直接可以看做年化r

1 个答案

李坏_品职助教 · 2023年09月08日

嗨,从没放弃的小努力你好:


答案解析里面把coupon已经调整为半年的coupon了,分别是4.25和5,所以N也要以半年为单位,半年对应N=1,一年对应N=2。


Bond A的PV = 98,完整的公式是98 = (100+4.25)/(1+y/2)^1,所以y_A = 12.76%。

BondB:101=5/(1+y/2) + (100+5)/(1+y/2)^2,所以y_B=8.93%


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