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A Random Field LIBOR Market Model

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  • Tao L. Wu
  • Shengqiang Xu

Abstract

A random field LIBOR market model (RFLMM) is proposed by extending the LIBOR market model, with interest rate uncertainties modeled via a random field. First, closed‐form formulas for pricing caplet and swaption are derived. Then the random field LIBOR market model is integrated with the lognormal‐mixture model to capture the implied volatility skew/smile. Finally, the model is calibrated to cap volatility surface and swaption volatilities. Numerical results show that the random field LIBOR market model can potentially outperform the LIBOR market model in capturing caplet volatility smile and the pricing of swaptions, in addition to possessing other advantages documented in the previous literature (no need of frequent recalibration or to specify the number of factors in advance). © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 34:580–606, 2014

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  • Tao L. Wu & Shengqiang Xu, 2014. "A Random Field LIBOR Market Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(6), pages 580-606, June.
    • Handle: RePEc:wly:jfutmk:v:34:y:2014:i:6:p:580-606
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Damiano Brigo & Fabio Mercurio, 2002. "Lognormal-Mixture Dynamics And Calibration To Market Volatility Smiles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 427-446.
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    4. Tao L. Wu, 2012. "Pricing and Hedging the Smile with SABR : Evidence from the Interest Rate Caps Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(8), pages 773-791, August.
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    6. Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-384.
    7. Francis A. Longstaff & Pedro Santa‐Clara & Eduardo S. Schwartz, 2001. "The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence," Journal of Finance, American Finance Association, vol. 56(6), pages 2067-2109, December.
    8. D. P. Kennedy, 1997. "Characterizing Gaussian Models of the Term Structure of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 107-118, April.
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    1. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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