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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

In a two-factor Gaussian model of the yield curve, the first factor typically produces parallel shifts and the second factor produces changes in slope. Which statement about the model's usefulness is most accurate compared with a one-factor model?

A multifactor model allows yields at different maturities to move with less than perfect correlation, such as through changes in slope, whereas a one-factor model forces all yields to be perfectly correlated. It still needs calibration and, if Gaussian, can produce negative rates.

  1. AIt makes all bond yields perfectly correlated
  2. BIt allows imperfect correlation between yields at different maturitiesCorrect
  3. CIt removes the need to calibrate any parameters
  4. DIt guarantees that interest rates can never be negative
  5. It eliminates all arbitrage opportunities regardless of calibration

Explanation

A one-factor model makes changes in all rates driven by one source of risk, so yields at different maturities are perfectly correlated. Adding a second factor allows twists and imperfect correlation. Gaussian models do allow negative rates, and calibration is still required.

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