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Approximations Of Bond And Swaption Prices In A Black–Karasiński Model

Author

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  • ANDRZEJ DANILUK

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

  • RAFAŁ MUCHORSKI

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

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.

Suggested Citation

  • Andrzej Daniluk & Rafał Muchorski, 2016. "Approximations Of Bond And Swaption Prices In A Black–Karasiński Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-32, May.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:03:n:s0219024916500175
    DOI: 10.1142/S0219024916500175
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    References listed on IDEAS

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    Cited by:

    1. Jaehyuk Choi, 2024. "Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo\`eve expansions," Papers 2402.09243, arXiv.org.
    2. Anna Knezevic, 2024. "Enhancing path-integral approximation for non-linear diffusion with neural network," Papers 2404.08903, arXiv.org.

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