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APPROXIMATIONS OF BOND AND SWAPTION PRICES IN A BLACK–KARASIŃSKI MODEL

ANDRZEJ DANILUK

Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Krakow, Poland

E-mail Address: andrzej.daniluk@gmail.com

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and

RAFAŁ MUCHORSKI

Risk Management Department, TUiR Allianz Polska SA, ul. Rodziny Hiszpańskich 1, 02-685 Warsaw, Poland

E-mail Address: rafal.muchorski@gmail.com

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https://doi.org/10.1142/S0219024916500175Cited by:13 (Source: Crossref)

Abstract

We derive semi-analytic approximation formulae for bond and swaption prices in a Black–Karasiński (BK) interest rate model. Approximations are obtained using a novel technique based on the Karhunen–Loève 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.

Keywords:

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