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

A risk manager reviews a model in which the short rate follows dr = lambda(t) dt + sigma dw under the risk-neutral measure. The manager notes that when the initial curve is steeply upward sloping, lambda(t) is large for long dates. What does a larger lambda(t) at a future date imply for the model?

A larger drift at a future date means the risk-neutral expected short rate is higher then, consistent with a higher forward rate once the convexity adjustment is accounted for. It does not change volatility, which is set by sigma, and the model has no mean reversion.

  1. AThe expected short rate at that date is higher under the risk-neutral measure, consistent with a higher forward rate adjusted for convexityCorrect
  2. BThe volatility of the short rate is higher at that date
  3. CThe short rate will mean revert faster toward zero
  4. DBond prices at that date must be higher than the market implies

Explanation

Drift is the expected change in the short rate under the risk-neutral measure. An upward-sloping forward curve requires a rising expected path, so lambda(t) is larger, with a convexity adjustment linked to sigma. It says nothing about volatility level or mean reversion speed in this model.

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