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Approximate pricing of swaptions in affine and quadratic models

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  • Anna Maria Gambaro
  • Ruggero Caldana
  • Gianluca Fusai

Abstract

This paper proposes new bounds on the prices of European-style swaptions for affine and quadratic interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known. In particular, our lower bound involves the computation of a one-dimensional Fourier transform independently of the swap length. In addition, we control the error of our method by providing a new upper bound on swaption price that is applicable to all considered models. We test our bounds on different affine models and on a quadratic Gaussian model. We also apply our procedure to the multiple curve framework. The bounds are found to be accurate and computationally efficient.

Suggested Citation

  • Anna Maria Gambaro & Ruggero Caldana & Gianluca Fusai, 2017. "Approximate pricing of swaptions in affine and quadratic models," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1325-1345, September.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:9:p:1325-1345
    DOI: 10.1080/14697688.2017.1292043
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    References listed on IDEAS

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    1. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements.
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    Cited by:

    1. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    2. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2019. "Multiple yield curve modelling with CBI processes," Papers 1911.02906, arXiv.org, revised Oct 2020.

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