8008 Exam Dumps | If the annual default hazard rate for a borrower is 10%, what is the probability that there is no default

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PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition
PRMIA.8008.v2021-08-28.q125
Question 48

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Question 48/125

If the annual default hazard rate for a borrower is 10%, what is the probability that there is no default at the end of 5 years?

A. 39.35%

B. 50.00%

C. 59.05%

D. 60.65%

Correct Answer: D

Explanation
A default hazard rate is the rate of default in a continuous time setting. This question is asking for probability of survival at the end of 5 years. The formula to calculate the probability of survival at the end of t years where the default hazard rate is is e^(- *t) (or in Excel, =exp(-*t). Therefore the correct answer is Choice 'd'.
(It may be tempting to infer that if the probability of survival at the end of 1 year is 90% (1 - 10%), then the probability of survival in 5 years would be 90%^5. However this reasoning is not correct for the reason that the given rate is not the discrete rate of default, but the hazard rate which is nothing but the continuously compounded rate of default.)

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