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Time-Changed Lévy LIBOR Market Model: Pricing and Joint Estimation of the Cap Surface and Swaption Cube

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  • Markus Leippold

    (University of Zurich, Ecole Polytechnique Fédérale de Lausanne, and Swiss Finance Institute)

  • Jacob Stromberg

    (Swiss Finance Institute)

Abstract

We propose a novel time-changed Lévy LIBOR market model for the joint pricing of caps and swaptions. The time changes are split into three components. The first component allows us to match the volatility term structure, the second generates stochastic volatility, and the third one accommodates for stochastic skew. The model is parsimonious, yet flexible enough to accommodate the behavior of both caps and swaptions well. For the joint estimation we use a comprehensive dataset spanning the recent financial crisis. We find that, even during the recent financial crisis, neither market is as fragmented as suggested by the previous literature.

Suggested Citation

  • Markus Leippold & Jacob Stromberg, 2012. "Time-Changed Lévy LIBOR Market Model: Pricing and Joint Estimation of the Cap Surface and Swaption Cube," Swiss Finance Institute Research Paper Series 12-23, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1223
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    Cited by:

    1. Ming-Chieh Wang & Li-Jhang Huang, 2019. "Pricing cross-currency interest rate swaps under the Levy market model," Review of Derivatives Research, Springer, vol. 22(2), pages 329-355, July.
    2. Gong, Xiao-Li & Liu, Jian-Min & Xiong, Xiong & Zhang, Wei, 2022. "Research on stock volatility risk and investor sentiment contagion from the perspective of multi-layer dynamic network," International Review of Financial Analysis, Elsevier, vol. 84(C).
    3. Zhanyu Chen & Kai Zhang & Hongbiao Zhao, 2022. "A Skellam market model for loan prime rate options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 525-551, March.

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    More about this item

    Keywords

    LIBOR market models; time-changed Lévy process; caps volatilities; swaption cube; unscented Kalman filter;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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