FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A two-factor Gaussian model has short rate r = x1 + x2, where the factors have instantaneous volatilities of 90 bps and 60 bps per year and instantaneous correlation of -0.5 between their shocks. What is the instantaneous volatility of the short rate?
The short rate volatility is the square root of 90² + 60² + 2×(-0.5)×90×60, which is the square root of 6,300, roughly 79 bps, so about 78 bps is the closest choice. Simply adding volatilities or ignoring the negative correlation would overstate it.
- AAbout 78 bpsCorrect
- BAbout 150 bps
- CAbout 108 bps
- DAbout 30 bps
Explanation
Variance = 90² + 60² + 2(-0.5)(90)(60) = 8,100 + 3,600 - 5,400 = 6,300. Square root is about 79.4 bps; nearest option is about 78 bps. Adding volatilities (150) ignores correlation; omitting the covariance gives sqrt(11,700)≈108.
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