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Answer: 78.7%
## Explanation Under the stressed scenario: - Spread = 480 bps = 480/10000 = 0.048 - Recovery Rate (RR) = 40% = 0.40 - Loss Given Default (LGD) = 1 - RR = 1 - 0.40 = 0.60 **Step 1: Calculate the hazard rate (λ)** The hazard rate formula is: \[\lambda = \frac{spread}{1 - RR} = \frac{0.048}{0.60} = 0.08\] **Step 2: Calculate the survival probability over 3 years** Using the constant hazard rate process: \[P(survival) = e^{-\lambda t} = e^{-0.08 \times 3} = e^{-0.24} = 0.7866 = 78.66\%\] **Why other options are incorrect:** - **A (69.8%)**: Incorrectly uses the recovery rate instead of LGD in the hazard rate formula - **C (86.6%)**: Incorrectly takes hazard rate per year as 4.8% (ignoring recovery rate) - **D (74.1%)**: Incorrectly uses the original spread (250 bps) and recovery rate (75%) instead of the stressed scenario parameters The correct answer is **78.7%** (rounded from 78.66%).
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The head of the fixed-income department of a bank asks a risk analyst to review an outstanding bond issued by Company GRN, a livestock producer. The bond currently trades at a spread of 250 bps over the risk-free interest rate and has a recovery rate of 75%. Senior management of the bank has expressed concern about the slowdown in business activities in the livestock industry, which is expected to last for the next 3 years. The analyst applies the constant hazard rate process in estimating default probability and assumes that, under a stressed market scenario, the bond would trade at a spread of 480 bps over the risk-free interest rate curve, and its recovery rate would decrease to 40%. Assuming the stress scenario prevails, what would be the correct estimate of the probability that Company GRN would not default on its bond over the next 3 years?
A
69.8%
B
78.7%
C
86.6%
D
74.1%