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A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach


  • Atsushi Kawai


This paper presents a new approximate pricing formula for European payer swaptions in the LIBOR market model using an asymptotic expansion method. The formula is very flexible, since it can be applied to a wide range of volatility functions. The formula is tested with a log-normal volatility function and a modified CEV volatility function. Numerical results show that the proposed approximate formula is more accurate than other approximate formulae.

Suggested Citation

  • Atsushi Kawai, 2003. "A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 49-74.
  • Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:49-74 DOI: 10.1080/1350486021000029216

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    References listed on IDEAS

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    Cited by:

    1. Akihiko Takahashi & Kohta Takehara, 2007. "An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 69-121, March.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    3. Kenichiro Shiraya & Akihiko Takahashi & Akira Yamazaki, 2010. "Pricing Swaptions under the Libor Market Model of Interest Rates with Local-Stochastic Volatility Models," CARF F-Series CARF-F-214, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Xu, Guoping & Zheng, Harry, 2010. "Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 415-422, December.
    5. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.


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