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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

In Tuckman's Model 1, the short-term rate follows dr = σ dw with no drift, where σ is constant and dw is a normal random variable with mean zero. A risk analyst is asked to describe the model's implications. Which statement is correct?

In Model 1 the drift is zero, so the expected future short rate equals today's rate at all horizons. Because shocks are normally distributed, the rate can fall below zero. There is no mean reversion, which distinguishes it from the Vasicek model.

  1. AThe expected future short rate equals today's short rate at every horizon, and the rate can become negativeCorrect
  2. BThe expected future short rate declines over time at a rate set by σ, and the rate cannot become negative
  3. CThe expected future short rate reverts to a long-run mean, and the rate cannot become negative
  4. DThe expected future short rate equals today's short rate, and the rate cannot become negative because volatility is constant

Explanation

With zero drift, the change in the rate has mean zero, so the expected future rate equals the current rate at all horizons. The shock is normally distributed, so the rate has a positive probability of being negative. Mean reversion is not present in Model 1; it appears in the Vasicek model.

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