Approximations of Bond and Swaption Prices in a Black-Karasi\'nski Model
Abstract
We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasi\'nski interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Lo\`eve 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.
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