Approximating the zero-coupon bond price in a general one-factor model with constant coefficients

We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around $\tau=0$, where $\tau$ is time to maturity. We provide numerical examples of convergence of the partial sums of the series and compare them with the known exact values in the case of Cox-Ingersoll-Ross and Dothan model.