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

A risk manager uses Model 1 with σ = 0.90% per year. The one-year-ahead short rate is simulated using monthly steps (Δt = 1/12). Which statement about the variance of the short rate after 12 steps is correct?

The variance after twelve monthly steps equals σ² times one year, or 0.81 squared percent. Each step contributes σ² times 1/12 and independent normal increments add, so the total standard deviation is 0.90%, independent of the step size.

  1. AIt equals 12 × σ² × (1/12) = σ², i.e. 0.81 (%)²Correct
  2. BIt equals 12 × σ² = 9.72 (%)²
  3. CIt equals σ² × (1/12) = 0.0675 (%)²
  4. DIt is larger than σ² because shocks compound multiplicatively

Explanation

Each monthly step adds variance σ²Δt = 0.81/12 (%)². Independent increments sum over 12 steps to 0.81 (%)², so standard deviation is 0.90%. Ignoring Δt gives 9.72, a wrong scaling error. Compounding does not apply to additive shocks.

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