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

An actuary calibrates a Vasicek model dr = a(μ − r)dt + σ dW to daily observations of the 91-day T-bill yield. Which statement about the practical use of the calibrated model is correct?

Because the Vasicek short rate is normally distributed, simulated rates can go negative with positive probability, which may be unsuitable in some applications. Historical calibration gives real-world parameters, volatility is constant, and the long-run mean is a free parameter rather than the current rate.

  1. AThe model can never produce negative interest rates because the drift pulls rates upward
  2. BBecause the model is Gaussian, simulated short rates can become negative, which may be unacceptable for some applicationsCorrect
  3. CCalibration to historical data automatically gives the risk-neutral parameters needed for pricing
  4. DThe long-run mean μ is fixed by the model to equal the current short rate
  5. The volatility σ falls as the short rate falls

Explanation

In Vasicek the short rate is normally distributed, so negative rates have positive probability. Historical (real-world) calibration does not give risk-neutral parameters without a market price of risk adjustment. Volatility is constant in Vasicek, and μ is a free parameter.

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