FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A analyst notes that the Vasicek model assumes constant σ and normally distributed short rate changes. Which is a direct consequence of this specification?
Because Vasicek uses constant volatility and normal shocks, the short rate is normally distributed, so it can become negative with positive probability. Models with volatility proportional to the rate level, like CIR, avoid this, but Vasicek does not.
- AThe short rate can become negative with positive probabilityCorrect
- BThe short rate can never fall below zero
- CThe volatility of the short rate rises in proportion to the rate level
- DThe short rate has no tendency to revert to a mean
Explanation
With constant volatility and normal shocks, the short rate is normally distributed, so negative values have positive probability. Rate-proportional volatility belongs to the CIR or lognormal models, not Vasicek. Vasicek does have mean reversion.
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