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

A Vasicek model has k = 0.25, θ = 4%, and current short rate r0 = 6%. Ignoring risk premium and convexity, what is the expected short rate after 2 years? Use e^(−0.5) = 0.6065.

The expected short rate after two years is about 5.21%. Using the Vasicek formula, the 2% gap between 6% and the 4% long-run level decays by e^(−0.25×2)=0.6065, leaving 1.21%, which is added to 4%.

  1. A4.79%Correct
  2. B5.21%
  3. C5.39%
  4. D4.00%

Explanation

E[r2] = θ + (r0 − θ)e^(−kt) = 4% + 2% × 0.6065 = 5.213%. Wait: 2% × 0.6065 = 1.213%, giving 5.21%.

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