FRM Part I · FRM Exam Part I · Measuring Credit Risk
In a reduced-form (intensity-based) model, default is modeled as the first jump of a Poisson process with a constant hazard rate of 2% per year. What is the probability that the firm survives for 5 years and then defaults during year 6 (i.e., between t=5 and t=6)?
The probability is about 1.79%, which is closest to 1.81%. It equals survival to year 5, e^(-0.10), times the conditional year-6 default probability, 1 - e^(-0.02), or e^(-0.10) - e^(-0.12) ≈ 0.0179.
- A1.81%Correct
- B2.00%
- C9.52%
- D1.63%
Explanation
Survival to 5 years is e^(-0.10)=0.904837. Probability of default in year 6 given survival = 1 - e^(-0.02) = 0.019801. Product = 0.904837 × 0.019801 = 0.017917, about 1.79%; equivalently e^(-0.10) - e^(-0.12) = 0.904837 - 0.886920 = 0.017917.
Did you get it right without looking?
One question tells you little. A timed set on Measuring Credit Risk shows your real accuracy, how long you take and where you lose marks.
More Measuring Credit Risk questions
- Which of the following best explains why a loan portfolio's unexpected loss is generally less than the sum of the stand-alone unexpected los…
- A one-year transition matrix gives a B-rated issuer a 10% chance of default, 70% chance of remaining B, and 20% chance of upgrade to BB. A B…
- Holding all other Merton model inputs constant, the volatility of a firm's assets increases. Which outcome is correct?
- A bank has a single loan with exposure at default of 10,000,000. The one-year probability of default is 2% and the loss given default is 60%…
- Which statement about the Markov assumption in rating transition matrices is correct?
- A bank's one-year rating transition matrix shows that a BB-rated obligor has a 4% probability of moving to B, 88% of staying at BB, 6% of up…