Using perturbation methods, approximate formulas are obtained for zero-coupon bonds under the generalized Black-Karasinski model. The formulas perform well regarding accuracy and calibration to available data. For a special case, which corresponds to the Hull-White model, the approximation actually yields an exact solution. Numerical simulations are presented that partially validate the asymptotic approximation. A calibration strategy is investigated in order to fit the model to given data on discount rates.