Approximate Formulas for Zero‐coupon Bonds

Abstract

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...