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

A two-factor Gaussian model has a fast factor (mean-reversion speed 1.50) and a slow factor (speed 0.10). A shock hits both factors equally today. Which describes the effect on the yield curve after five years, relative to today?

After five years the fast factor's shock has nearly vanished, since exp(-1.5×5) is about 0.0006, while the slow factor retains about 61 percent, since exp(-0.1×5) is about 0.61. The remaining impact therefore comes mostly from the slow factor, which mean reverts much more gradually.

  1. AThe fast factor's effect is largely gone, so the remaining effect comes mostly from the slow factorCorrect
  2. BBoth factors' effects persist equally because the shocks are equal
  3. CThe slow factor's effect disappears faster than the fast factor's
  4. DBoth effects grow with time because variance accumulates

Explanation

Expected decay of a shock is exp(-kT). For T=5, the fast factor gives exp(-7.5), about 0.0006, while the slow factor gives exp(-0.5), about 0.61. So the slow factor dominates the remaining impact. Equal initial shocks do not mean equal persistence.

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