Skip to content

FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

In a two-factor Gaussian model, the short rate is r = x1 + x2, where x1 and x2 are independent and mean-reverting with zero long-run mean. The factor volatilities are 80 bp and 60 bp per year (annualized, stationary-level volatilities for simplicity). What is the annualized standard deviation of the short rate under this simplification?

The short rate's standard deviation is 100 basis points. With independent factors, variances add: 80 squared plus 60 squared equals 10,000, whose square root is 100. Simply adding the volatilities to get 140 basis points would wrongly assume perfect correlation.

  1. A140 bp
  2. B100 bpCorrect
  3. C70 bp
  4. D20 bp

Explanation

For independent factors, variances add: 80^2 + 60^2 = 6,400 + 3,600 = 10,000, so the standard deviation is 100 bp. Adding the volatilities (140 bp) wrongly ignores that independent risks combine in quadrature.

Did you get it right without looking?

One question tells you little. A timed set on The Vasicek and Gauss+ Models shows your real accuracy, how long you take and where you lose marks.

Practise The Vasicek and Gauss+ ModelsFree diagnostic mock

More The Vasicek and Gauss+ Models questions