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

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  • Andrzej Daniluk
  • Rafa{l} Muchorski

Abstract

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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  • Andrzej Daniluk & Rafa{l} Muchorski, 2015. "Approximations of Bond and Swaption Prices in a Black-Karasi\'{n}ski Model," Papers 1506.00697, arXiv.org.
    • Handle: RePEc:arx:papers:1506.00697
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