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Approximate Formulas for Zero-coupon Bonds

Author

Listed:
  • Fabricio Tourrucoo
  • Patrick S. Hagan
  • Gilberto F. Schleiniger

Abstract

Using perturbation methods, approximate formulas are obtained for zero-coupon bonds under the generalized Black-Karasinski model. The formulas perform well regarding accuracy and calibration to available data. For a special case, which corresponds to the Hull-White model, the approximation actually yields an exact solution. Numerical simulations are presented that partially validate the asymptotic approximation. A calibration strategy is investigated in order to fit the model to given data on discount rates.

Suggested Citation

  • Fabricio Tourrucoo & Patrick S. Hagan & Gilberto F. Schleiniger, 2007. "Approximate Formulas for Zero-coupon Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 207-226.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:3:p:207-226
    DOI: 10.1080/13504860600858204
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    References listed on IDEAS

    as
    1. Patrick Hagan & Diana Woodward, 1999. "Equivalent Black volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 147-157.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
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    Cited by:

    1. Beáta Stehlíková, 2021. "New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation," Mathematics, MDPI, vol. 9(13), pages 1-10, June.
    2. Zura Kakushadze, 2015. "Coping with Negative Short-Rates," Papers 1502.06074, arXiv.org, revised Aug 2015.
    3. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    4. 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.
    5. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion," Papers 2306.09084, arXiv.org.
    6. Dan Pirjol, 2015. "Hogan-Weintraub singularity and explosive behaviour in the Black-Derman-Toy model," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1243-1257, July.
    7. Andrzej Daniluk & Rafa{l} Muchorski, 2015. "Approximations of Bond and Swaption Prices in a Black-Karasi\'{n}ski Model," Papers 1506.00697, arXiv.org.

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