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23. Consider the following homogeneous reference portfolio in a synthetic collateralized debt obligation:

   ·Number of reference entities:      100

   ·Credit default swap (CDS) spread:  150 bps

   ·Recovery rate in case of default:  50%

Assume that defaults are independent. On a single name the annual default probability is constant over five years and obeys the relation: CDS Premium = (1- Recovery rate) * Annual Default Probability

What is the expected number of defaulting entities over the next five years, and which of the following tranches would be entirely wiped out (loses 100% of the principal invested) by the expected number of defaulting entities?

a.        14 defaults and a [3% - 14%] tranche would be wiped out

b.       3 defaults and a [0% - 1%] tranche would be wiped out

c.       7 defaults and a [2% -3%] tranche would be wiped out

d.       14 defaults and a [6% -7%] tranche would be wiped out

答案选d，请问6-7% tranche是如何算出来的

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关键词：CDS Probability Independent homogeneous Collateral following reference defaults expected relation

个人理解，3%的违约率已经算出来，5年之后还剩85.8，约为14家淘汰，其中违约收回本金50%，因此约7%本金被去除，求奖励