FRM Part I · FRM Exam Part I · Common Univariate Random Variables
Defaults in a bond portfolio arrive as a Poisson process at a rate of 0.5 per quarter. Assuming independence across periods, what is the probability of at least one default over a six-month (two-quarter) period? (Use e^-1 = 0.3679.)
The probability is 0.6321. Scaling the rate to six months gives lambda = 1, so the chance of no defaults is e^-1 = 0.3679, and the chance of at least one default is one minus that, or 0.6321.
- A0.6321Correct
- B0.3935
- C0.3679
- D0.2642
Explanation
Over two quarters lambda = 0.5 x 2 = 1. P(at least one) = 1 - e^-1 = 1 - 0.3679 = 0.6321. Using lambda = 0.5 for the period gives 0.3935 (failure to scale the rate). 0.3679 is the probability of no default.
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