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Options on bonds: implied volatilities from affine short-rate dynamics

Author

Listed:
  • Matthew Lorig

    (University of Washington)

  • Natchanon Suaysom

    (University of Washington)

Abstract

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical experiments in order to gauge the accuracy of our approximation.

Suggested Citation

  • Matthew Lorig & Natchanon Suaysom, 2022. "Options on bonds: implied volatilities from affine short-rate dynamics," Annals of Finance, Springer, vol. 18(2), pages 183-216, June.
    • Handle: RePEc:kap:annfin:v:18:y:2022:i:2:d:10.1007_s10436-022-00407-w
    DOI: 10.1007/s10436-022-00407-w
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    References listed on IDEAS

    as
    1. Stefano Pagliarani & Andrea Pascucci, 2017. "The exact Taylor formula of the implied volatility," Finance and Stochastics, Springer, vol. 21(3), pages 661-718, July.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. 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.
    4. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
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    Cited by:

    1. Qi Zhang & Qi Wang & Ping Zuo & Hongbo Du & Fangfang Wu, 2023. "Projection and Contraction Method for Pricing American Bond Options," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    2. Matthew Lorig & Natchanon Suaysom, 2022. "Explicit Caplet Implied Volatilities for Quadratic Term-Structure Models," Papers 2212.04425, arXiv.org.

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    More about this item

    Keywords

    Affine short-rate; Implied volatility; Options on bonds;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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