Skip to content

FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

In a Vasicek model with k = 0.25 and σ = 2.00% (annual), what is the standard deviation of the short rate at a horizon of 2 years, as seen from today? Use Var[r(T)] = σ²(1 − e^(−2kT))/(2k).

The standard deviation is 2.25%. Variance is σ²(1 − e^(−2kT))/(2k) = 0.0004 × 0.632/0.5 = 0.000506. Mean reversion keeps it below the no-reversion figure of 2.83%, which would be σ√T, and above the 2.00% one-year-instant volatility.

  1. A2.25%Correct
  2. B2.83%
  3. C2.00%
  4. D1.77%

Explanation

2kT = 0.25×2×2/2... computing directly: 2kT = 2×0.25×2 = 1. Variance = 0.0004 × (1 − e^−1)/0.5 = 0.0004 × 0.63212/0.5 = 0.0005057. The square root is 2.25%. The 2.83% option is σ√T with no mean reversion. The 1.77% option uses e^(−kT) instead of e^(−2kT).

Did you get it right without looking?

One question tells you little. A timed set on The Vasicek and Gauss+ Models shows your real accuracy, how long you take and where you lose marks.

Practise The Vasicek and Gauss+ ModelsFree diagnostic mock

More The Vasicek and Gauss+ Models questions