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On the American swaption in the linear-rational framework

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  • Damir Filipović
  • Yerkin Kitapbayev

Abstract

We study American swaptions in the linear-rational (LR) term structure model introduced in Filipović et al. [J. Finance., 2017, 72, 655–704]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus of Peskir [J. Theoret. Probab., 2005a, 18, 499–535]. We characterize the optimal stopping boundary as the unique solution to a non-linear integral equation that can be readily solved numerically. We obtain the arbitrage-free price of the American swaption and the optimal exercise strategies in terms of swap rates for both fixed-rate payer and receiver swaps. Finally, we show that Bermudan swaptions can be efficiently priced as well.

Suggested Citation

  • Damir Filipović & Yerkin Kitapbayev, 2018. "On the American swaption in the linear-rational framework," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1865-1876, November.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:11:p:1865-1876
    DOI: 10.1080/14697688.2018.1446547
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    Cited by:

    1. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
    2. Frédéric Vrins & Linqi Wang, 2023. "Asymmetric short-rate model without lower bound," Quantitative Finance, Taylor & Francis Journals, vol. 23(2), pages 279-295, February.

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