Cox-Ingersoll-Ross (CIR) model incorporates the basis point volatility increases proportionally to the square root of the rate (i.e., σ√r) and dr increases at a decreasing rate, and σ is constant.
The CIR model is as follows: dr = k(θ − r)dt + σ√r dw.
The lognormal model shows that basis point volatility increases with the short-term rate. An important property of the lognormal model is that the yield volatility, σ, is constant, but basis point volatility increases with the level of the short-term rate.
Specifically, basis point volatility is equal to σr and the functional form of the model, where σ is constant and dr increases at σr, is:
dr = ardt + σrdw
Why is COX-INGERSOLL-ROSS (CIR) important?
For both the CIR and the lognormal models, if the short-term rate is not negative, a positive drift implies that the short-term rate cannot become negative.