The credit spreads for a counterparty for 5 and 6 years are 2% and 2.2% respectively. The recovery rate is 60%. What is closest to the unconditional default probability for the sixth year?
A. 0.04
B. 0.05
C. 0.06
D. 0.07
C
The average hazard rate for the first five years is 0.02/(1-0.6)=0.05 or 5%. The average hazard rate for the first six years is 0.022/(1-0.6)=0.055 or 5.5%. The probability of no default during the first five years is therefore e-0.05×5=0.7788 . The probability of no default during the first six years is e-0.055×6 =0.7189 . The probability of default during the sixth year is therefore 0.7788−0.7189 or approximately 0.06.
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