NO.PZ2020033002000008
问题如下:
There is a bond portfolio consisted with two bonds. bond A and bond B .The values of bond A and bond B are $60 millions and $40 millions respectively. The one-year probabilities of default and the recovery rate of bond A are 5% and 60% respectively, while for bond B are 7% and 50%. Give an assumption that the probability of joint default is 0.5% and the default correlation is 20%. what is the best estimate of the credit VaR at a 98% confidence level?
选项:
A.USD 17,400,000
B.USD 21,400,000
C.USD 41,400,000
D.USD 44,000,000
解释:
B is correct.
考点:Credit VaR
解析:
Bond A 违约的损失是60*(1-60%)=24 million
Bond B违约的损失是40*(1-50%)=20million
A、 B同时违约的概率是 0.5%
Bond A 违约但是bond B不违约的概率是 5%-0.5%=4.5%
Bond B违约但是bond A不违约的概率是7%-0.5%=6.5%
根据谨慎性原则 98% confidence WCL=24million
credit VaR=24-2.6=21.4 million
想问一下 同时违约的话 那不应该是 Probability loss(小于等于100)=99.5% 而Probability Loss(A=60)=95.5% 所以98%是夹在两个之间 那么谨慎性原则应该取100m?