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Pricing Swaptions under the Libor Market Model of Interest Rates with Local-Stochastic Volatility Models

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  • Kenichiro Shiraya

    (Mizuho-DL Financial Technology Co.,Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Akira Yamazaki

    (Mizuho-DL Financial Technology Co.,Ltd.)

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    Abstract

    This paper presents a new approximation formula for pricing swaptions and caps/floors under the LIBOR market model of interest rates (LMM) with the local and affine-type stochastic volatility. In particular, two approximation methods are applied in pricing, one of which is so called gdrift-freezingh that fixes parts of the underlying stochastic processes at their initial values. Another approximation is based on an asymptotic expansion approach. An advantage of our method is that those approximations can be applied in a unified manner to a general class of local-stochastic volatility models of interest rates. To demonstrate effectiveness of our method, the paper takes CEVHeston LMM and Quadratic-Heston LMM as examples; it confirms sufficient flexibility of the models for calibration in a caplet market and enough accuracies of the approximation method for numerical evaluation of swaption values under the models.

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    File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/266.pdf
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    Bibliographic Info

    Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-255.

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    Length: 32 pages
    Date of creation: Oct 2011
    Date of revision:
    Handle: RePEc:cfi:fseres:cf255

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