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大白 · 2021年08月04日

274.805怎么算的

NO.PZ2019011002000003

问题如下:

Tim, a credit analyst, is valuing bond C. Bond C is rated at AA. Bond C is a 5-year corporate bond with a par value of $1000. The bond has a fixed annual coupon rate of 6%, and the coupon is paid annually.

Tim believes that the risk-neutral probability of default (Hazard rate) for each date for the bond is 1.50%, and the recovery rate is 25%. Assume there is no interest rate volatility and the government bond yield curve is flat at 2%.

The market price of Bond C is $1087. If the bond is purchased at this price, and there is a default on Date 4, the rate of return to the bond buyer is closest to:

选项:

A.

-15%

B.

-46%

C.

-23%

解释:

C is correct.

考点:计算违约情况下债券的Return

解析:

该5年期债券,在第四年违约,计算投资者收益率可以通过计算IRR得到。

由于在第四年违约,第四年的现金流为第四年的Recovery value;

计算第四期的Recovery value,需要计算出第四期的Exposure,计算步骤和上题一致;有了第四期的Exposure乘以Recovery rate之后,可以得到本期的Recovery value。本题数据和上题一致,可从上题表格知,计算出来的Recovery value为:274.805

该债券在第四期违约,前三期的Coupon仍然可以拿到,因此IRR为:

1087=60(1+IRR)+60(1+IRR)2+60(1+IRR)3+274.805(1+IRR)41087=\frac{60}{(1+IRR)}+\frac{60}{(1+IRR)^2}+\frac{60}{(1+IRR)^3}+\frac{274.805}{(1+IRR)^4}

274.805怎么算的
1 个答案

WallE_品职答疑助手 · 2021年08月05日

嗨,努力学习的PZer你好:


Recovery value = exposure × recovery rate,其中exposure就是在某个时间点投资者的总头寸。我们现在要算的是第四年的exposure即第四年的总头寸。那么就是第五年的现金流折现到第四年,加上第四年自己的coupon之后再一起乘以RR。也就是[1060/1.02+60]*25%=274.80,所以第四年的回收金额为274.80


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努力的时光都是限量版,加油!

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