We present an analytic pricing kernel for a two-factor Black-Karasinski (lognormal) short rate model as a rapidly convergent perturbation expansion valid in the limit of low rates. Even the leading order expansion is found to be extremely accurate in most circumstances. We use this expansion to derive analytic formulae for conditional bond prices and thus for zero rates and forward rates. The model is equally applicable for the modelling of credit spreads and satisfies the important requirement of guaranteeing positive implied default probabilities. We suggest how these results could be used for interest rate and credit spread scenario generation in risk capital calculations and provide some representative scenario calculations.