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Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?

Author

Listed:
  • Feng Zhao
  • Robert Jarrow
  • Haitao Li

Abstract

Using more than two years of daily interest rate cap price data, this paper provides a systematic documentation of a volatility smile in cap prices. We find that Black (1976) implied volatilities exhibit an asymmetric smile (sometimes called a sneer) with a stronger skew for in-the-money caps than out-of-the-money caps. The volatility smile is time varying and is more pronounced after September 11, 2001. We also study the ability of generalized LIBOR market models to capture this smile. We show that the best performing model has constant elasticity of variance combined with uncorrelated stochastic volatility or upward jumps. However, this model still has a bias for short- and medium-term caps. In addition, it appears that large negative jumps are needed after September 11, 2001. We conclude that the existing class of LIBOR market models can not fully capture the volatility smile

Suggested Citation

  • Feng Zhao & Robert Jarrow & Haitao Li, 2004. "Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?," Econometric Society 2004 North American Winter Meetings 431, Econometric Society.
    • Handle: RePEc:ecm:nawm04:431
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    Cited by:

    1. Eymen Errais & Fabio Mercurio, 2005. "Yes, Libor Models can capture Interest Rate Derivatives Skew : A Simple Modelling Approach," Computing in Economics and Finance 2005 192, Society for Computational Economics.
    2. Matheus R Grasselli & Tsunehiro Tsujimoto, 2011. "Calibration of Chaotic Models for Interest Rates," Papers 1106.2478, arXiv.org.
    3. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    4. Konstantinidi, Eirini & Skiadopoulos, George, 2011. "Are VIX futures prices predictable? An empirical investigation," International Journal of Forecasting, Elsevier, vol. 27(2), pages 543-560, April.
    5. Christopher Gust & Edward Herbst & David López-Salido & Matthew E. Smith, 2017. "The Empirical Implications of the Interest-Rate Lower Bound," American Economic Review, American Economic Association, vol. 107(7), pages 1971-2006, July.
    6. Jiang, George & Yan, Shu, 2009. "Linear-quadratic term structure models - Toward the understanding of jumps in interest rates," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 473-485, March.
    7. Szu, Wen-Ming & Wang, Ming-Chun & Yang, Wan-Ru, 2011. "The determinants of exchange settlement practices and the implication of volatility smile: Evidence from the Taiwan Futures Exchange," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 826-838, October.
    8. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    9. Christopher J. Gust & Edward P. Herbst & J. David López-Salido & Matthew E. Smith, 2012. "The Empirical Implications of the Interest-Rate Lower Bound," Finance and Economics Discussion Series 2012-83, Board of Governors of the Federal Reserve System (U.S.).
    10. Anders B. Trolle & Eduardo S. Schwartz, 2006. "A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives," NBER Working Papers 12337, National Bureau of Economic Research, Inc.
    11. Deuskar, Prachi & Gupta, Anurag & Subrahmanyam, Marti G., 2008. "The economic determinants of interest rate option smiles," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 714-728, May.
    12. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.

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    More about this item

    Keywords

    LIBOR market models; volatility smile; interest rate caps;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets

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