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Answer: 1.90%
The unconditional default probability during year 5 of the loan is calculated using the hazard rate model. The formula provided in the file content is: \[ \text{Unconditional Default Probability} = \exp(-h_4 \times 4) - \exp(-h_5 \times 5) \] where \( h_4 \) and \( h_5 \) are the average hazard rates between the present time and the end of year 4 and end of year 5, respectively. To find the unconditional default probability for year 5, we first need to determine the survival rate to the end of year 5, which is given by: \[ \text{Survival Rate to Year 5} = 1 - \text{Cumulative Default Probability to Year 5} = 1 - 0.062 = 0.938 \] The survival rate to the end of year 4 can be calculated using the average hazard rate for the first 4 years: \[ \exp(-0.011 \times 4) = 0.956954 \] Now, we can calculate the unconditional default probability for year 5: \[ \text{Unconditional Default Probability} = 0.956954 - 0.938 = 0.01895 \text{ or } 1.895\% \] This calculation leads us to the correct answer, which is option C, 1.90%. The other options provided incorrect calculations or interpretations of the survival rate and the unconditional default probability.
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A wholesale bank's credit risk analyst is evaluating the annual likelihood of default for a corporate borrower who has recently been granted a 5-year loan. By examining data provided by rating agencies, the analyst discovers that the cumulative probability of default over a 5-year period for bonds issued under similar conditions and of equivalent seniority by the borrower is 6.2%. This cumulative default probability is used to calculate the borrower's survival rate over the 5-year period. Furthermore, it is known that the borrower's average hazard rate for the first four years of the loan is 1.1%. Based on this information, what is the probability that the borrower will default during the fifth year of the loan, without being subject to any prior conditions?
A
1.71%
B
1.80%
C
1.90%
D
1.98%