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 has volatility 80 bps per year and x2 has volatility 60 bps per year, and the factors are independent. What is the instantaneous volatility of the short rate?
The short rate volatility is 100 basis points. With independent factors, variances add: 80 squared plus 60 squared equals 10,000, whose square root is 100. Simply summing the volatilities to 140 would require perfect correlation between the factors, which is not the case here.
- A140 bps
- B100 bpsCorrect
- C70 bps
- D20 bps
Explanation
Independent factors add in variance: 80^2 + 60^2 = 6400 + 3600 = 10000, so volatility is 100 bps. Adding volatilities (140) wrongly assumes perfect correlation. Averaging gives 70, and subtracting gives 20, neither of which follows from the variance rule.
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