Skip to content

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

A risk analyst compares two one-factor short-rate models calibrated to the same current term structure. Model A (Ho-Lee) has dr = λ(t)dt + σdw, and Model B (Vasicek) has dr = k(θ - r)dt + σdw. Which statement about the drift in these models is correct?

Ho-Lee uses a time-dependent drift λ(t) calibrated so the model reproduces the initial term structure, and it has no mean reversion. Vasicek instead has a mean-reverting drift with constant parameters, which generally cannot fit an arbitrary initial curve exactly.

  1. AHo-Lee has a time-dependent drift that lets it fit the initial curve exactly, and it has no mean reversionCorrect
  2. BHo-Lee has a drift that pulls rates toward a long-run level, while Vasicek has a drift that depends only on time
  3. CBoth models have zero drift under the real-world measure, so the drift plays no role in pricing
  4. DVasicek's drift is a function of time only, which lets it match any initial term structure exactly

Explanation

In Ho-Lee the drift λ(t) is a deterministic function of time chosen to match the initial curve, and rates have no mean reversion. Vasicek's drift pulls r toward θ at speed k, with constant parameters, so it generally cannot fit an arbitrary curve exactly. The options that swap these features are wrong.

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