Skip to content

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

A risk manager compares the long-horizon rate volatility in Ho-Lee (σ = 1.00%) and Vasicek (σ = 1.00%, k = 0.50). As the horizon T becomes very large, which description is correct?

Ho-Lee has no mean reversion, so its variance σ²T grows without limit. Vasicek's mean reversion bounds variance at σ²/(2k), which equals 0.0001 here. Hence only the first description is correct.

  1. AHo-Lee short-rate variance grows without bound, while Vasicek variance approaches σ²/(2k) = 0.01%Correct
  2. BBoth variances grow without bound, but Vasicek grows more slowly
  3. CBoth variances converge to a finite limit, with Vasicek's the larger
  4. DHo-Lee variance converges to σ²/(2k) while Vasicek variance grows linearly

Explanation

Ho-Lee variance is σ²T, which is unbounded. Vasicek variance is σ²(1 − e^(−2kT))/(2k), which tends to σ²/(2k) = 0.0001/(1.0) = 0.0001, i.e. 0.01% in variance (standard deviation 1%). Mean reversion therefore bounds the variance, so the option claiming unbounded growth in both is wrong.

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