问题如下:
Consider the following homogeneous reference portfolio in a synthetic CDO: number of reference entities, 100; CDS spread, ; recovery rate . Assume that defaults are independent. On a single name the annual default probability is constant over five years and obeys the relation: . What is the expected number of defaulting entities over the next five years, and which of the following tranches would be entirely wiped out (lose 100% of the principal invested) by the expected number of defaulting entities?
选项:
A. There would likely be 14 defaults and a [3%—14%] tranche would be wiped out.
B. There would likely be 3 defaults and a [0%—l%] tranche would be wiped out.
C. There would likely be 7 defaults and a [2 %—3%] tranche would be wiped out.
D. There would likely be 14 defaults and a [6%—7%] tranche would be wiped out.
解释:
ANSWER: D
The annual marginal PD is . Hence the cumulative PD for the five years is ,where the survival rates are , , and so on. The expected number of defaults is therefore , or 14. With a recovery rate of 50%, the expected loss is 7% of the notional. So, all the tranches up to the 7% point are wiped out.
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