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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution

Under Model 1 with σ = 1.20% per year and a 1-year horizon, the short rate has mean 4.00% at that horizon. Using the normal distribution, what is the probability (approximately) that the short rate falls below 1.60%? (Use z = 2 gives 2.28%, z = 1 gives 15.87%, z = 1.5 gives 6.68%.)

The probability is about 2.28%. The 1.60% level lies 2.40 percentage points below the 4.00% mean, which is two standard deviations of 1.20%. The normal cumulative probability at z of minus two is roughly 2.28%.

  1. A2.28%Correct
  2. B6.68%
  3. C15.87%
  4. D0.13%

Explanation

Standard deviation = 1.20% × √1 = 1.20%. z = (1.60 − 4.00)/1.20 = −2.0. The probability N(−2) = 2.28%. Choosing 15.87% would use z = −1, a mistake of dividing by 2.40% instead of the standard deviation.

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