Explanation

The unconditional default probability during year 5 is calculated using the formula:

$\exp\left(-\bar{h}_4 \times 4\right) - \exp\left(-\bar{h}_5 \times 5\right)$

Where:

• $\bar{h}_4$ = average hazard rate for first 4 years = 1.1% = 0.011
• $\bar{h}_5$ = average hazard rate over 5 years (unknown)

Step 1: Calculate 5-year survival rate

• 5-year cumulative default probability = 6.2% = 0.062
• 5-year survival rate = 1 - 0.062 = 0.938

Step 2: Calculate survival probability to end of year 4 $\exp(-0.011 \times 4) = \exp(-0.044) = 0.956954$

Step 3: Calculate unconditional default probability during year 5 $`$0.95`6954 - 0.93800 = 0.01895 \text{ or } 1.895%$$

Why other options are incorrect:

• A (1.71%): Incorrectly calculates survival rate as $\exp(-0.062) = 0.939883$
• B (1.80%): Incorrectly calculates as $0.062 - 4 \times 0.011$
• D (1.98%): This represents the conditional default probability during year 5

The correct answer is 1.90% (rounded from 1.895%).