We propose an analytic approximation formula for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a
volatility proportional to the power the interest rate itself. We derive its order of accuracy.
Afterwards, we suggest its use in calibration and show that it can be reduced to a simple optimization
problem. To test the calibration methodology, we use the simulated data from the Cox-Ingersoll-
Ross model where the exact bond prices can be computed. We show that using the approximation
in the calibration recovers the parameters with a high precision.