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

A risk manager is choosing between a one-factor Vasicek model and a Gauss+ model with three Gaussian factors to price and hedge a book of swaptions across different tenors. What is the principal advantage of the multifactor Gauss+ approach?

The main benefit of a Gauss+ multifactor model is that rates of different maturities are not perfectly correlated, so it can generate steepening, flattening and curvature changes, not just parallel shifts. A one-factor Vasicek model forces all rates to move together, which limits hedging and pricing realism.

  1. AIt allows rates at different maturities to move imperfectly correlated, so non-parallel curve shifts such as steepening and curvature changes can be generatedCorrect
  2. BIt eliminates the possibility of negative interest rates in all scenarios
  3. CIt makes the short rate follow a non-Gaussian distribution with fat tails
  4. DIt removes the need to calibrate to market prices of bonds

Explanation

A one-factor model makes all rates perfectly correlated, so only parallel-type moves in the driving factor occur. Multiple Gaussian factors permit level, slope and curvature-like shifts. Gauss+ remains Gaussian in its factors, so negative rates are still possible and fat tails are not produced by the Gaussian factors.

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