Skip to content

FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

A risk analyst compares two one-factor short-rate models calibrated to the same market data. Model A is the Ho-Lee model, dr = λ(t)dt + σ dw. Model B is the Vasicek model, dr = k(θ − r)dt + σ dw. Which statement about the drift of the two models is correct?

Ho-Lee uses a time-dependent drift λ(t) chosen to fit the initial term structure, with no mean reversion. Vasicek uses a drift k(θ − r) that pulls the short rate toward a constant long-run mean θ, so it reverts but does not fit the curve exactly.

  1. AHo-Lee has a time-dependent drift that lets it fit the initial term structure, while Vasicek has a mean-reverting drift toward a constant long-run levelCorrect
  2. BHo-Lee has a mean-reverting drift toward a constant level, while Vasicek has a time-dependent drift that fits the initial curve exactly
  3. CBoth models have drift that depends on the current short rate level
  4. DNeither model has a drift term because both assume a constant short rate

Explanation

In Ho-Lee the drift λ(t) is a function of time chosen to match the initial curve, with no dependence on r. In Vasicek the drift k(θ − r) pulls the rate toward constant θ. The other options reverse or misstate these features.

Did you get it right without looking?

One question tells you little. A timed set on Arbitrage Pricing with Term Structure Models shows your real accuracy, how long you take and where you lose marks.

Practise Arbitrage Pricing with Term Structure ModelsFree diagnostic mock

More Arbitrage Pricing with Term Structure Models questions