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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

An analyst uses the inverse transform method to simulate the time to default T of a firm, assumed exponential with CDF F(t) = 1 - exp(-0.05t), t in years. A uniform draw U = 0.60 is obtained. Using ln(0.4) = -0.9163, what is the simulated default time?

The simulated default time is about 18.3 years. Solving 0.60 = 1 - exp(-0.05T) gives exp(-0.05T) = 0.40, so T = -ln(0.40)/0.05 = 0.9163/0.05, which is roughly 18.33 years.

  1. A10.2 years
  2. B18.3 yearsCorrect
  3. C4.6 years
  4. D12.0 years

Explanation

Set U = F(T): 0.60 = 1 - exp(-0.05T), so exp(-0.05T) = 0.40. Then T = -ln(0.40)/0.05 = 0.9163/0.05 = 18.33 years. Using ln(0.6) = -0.5108 gives 10.2 years, which wrongly uses U in place of 1-U in the exponent.

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