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An Effective Approximation For Zero-Coupon Bonds And Arrow–Debreu Prices In The Black–Karasinski Model

Author

Listed:
  • BEÁTA STEHLÍKOVÁ

    (Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská Dolina, 842 25 Bratislava, Slovakia)

  • LUCA CAPRIOTTI

    (Quantitative Strategies, Credit Suisse, Eleven Madison Avenue, New York, NY 10010, USA)

Abstract

We present an accurate and easy-to-compute approximation of zero-coupon bonds and Arrow–Debreu (AD) prices for the Black–Karasinski (BK) model of interest rates or default intensities. Through this procedure, dubbed exponent expansion, AD prices are obtained as a power series in time to maturity. This provides remarkably accurate results — for time horizons up to several years — even when truncated to the first few terms. For larger time horizons the exponent expansion can be combined with a fast numerical convolution to obtain extremely accurate results.

Suggested Citation

  • Beáta Stehlíková & Luca Capriotti, 2014. "An Effective Approximation For Zero-Coupon Bonds And Arrow–Debreu Prices In The Black–Karasinski Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 1-16.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:06:n:s021902491450037x
    DOI: 10.1142/S021902491450037X
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    Citations

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    Cited by:

    1. 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.
    2. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.
    3. A. Itkin & A. Lipton & D. Muravey, 2020. "From the Black-Karasinski to the Verhulst model to accommodate the unconventional Fed's policy," Papers 2006.11976, arXiv.org, revised Jan 2021.
    4. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion," Papers 2306.09084, arXiv.org.

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