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

Andrzej Daniluk; Rafa{\l} Muchorski

arxiv: 1506.00697 · v1 · pith:VAMMNMOQnew · submitted 2015-06-01 · 💱 q-fin.CP

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

Andrzej Daniluk , Rafa{\l} Muchorski This is my paper

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keywords modelapproximationsblack-karasibondpricesswaptionaccurateapproximation

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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.

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