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

Under the Vasicek model, dr = a(b − r)dt + σ dW, which of the following statements is correct?

In the Vasicek model the short rate mean-reverts to b and is normally distributed, so negative rates are possible. It does not fit any initial yield curve automatically, and square-root volatility belongs to the CIR model instead.

  1. AThe short rate cannot become negative because of mean reversion
  2. BThe short rate is mean-reverting toward b and is normally distributed, so negative rates are possibleCorrect
  3. CThe short rate has a lognormal distribution and is always positive
  4. DThe model fits any observed initial yield curve exactly by construction
  5. The volatility of the short rate is proportional to the square root of r

Explanation

In Vasicek the short rate is an Ornstein–Uhlenbeck process, Gaussian at each time, so negative rates have positive probability. It reverts to b at speed a. It does not fit an arbitrary initial curve (Hull–White extends it to do so), and square-root volatility belongs to CIR.

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