Approximations of Bond and Swaption Prices in a Black-Karasi\'{n}ski Model

We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasi'{n}ski interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Lo`{e}ve expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for numerically efficient calibration of the model.