Skip to content

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

A desk calibrates a Ho-Lee model with σ = 1.00% to a flat market curve. The model's drift λ(t) is found to be rising over time even though the market curve is flat at 4%. What is the most appropriate explanation?

The drift rises to offset convexity. In Ho-Lee, the convexity effect of volatility pulls down yields more at longer maturities, so to match a flat market curve the expected short rate path must rise, approximately by σ²t. This is not mean reversion or arbitrage.

  1. AThe drift must offset the convexity effect, which grows with maturity, so that the expected short rate must rise to keep bond prices consistent with a flat curveCorrect
  2. BThe drift reflects mean reversion toward a higher long-run level
  3. CThe market curve must contain arbitrage opportunities
  4. DVolatility in Ho-Lee increases with maturity, requiring a rising drift to compensate for expected losses

Explanation

In Ho-Lee, the convexity term (about σ²t²/2 in the log bond price) lowers bond yields increasingly with maturity. To fit a flat curve, the drift must rise (approximately λ(t) ≈ forward rate slope + σ²t) to offset it. This is not mean reversion, arbitrage, or time-varying volatility.

Did you get it right without looking?

One question tells you little. A timed set on The Art of Term Structure Models: Drift shows your real accuracy, how long you take and where you lose marks.

Practise The Art of Term Structure Models: DriftFree diagnostic mock

More The Art of Term Structure Models: Drift questions