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

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  • ROBERT JARROW
  • HAITAO LI
  • FENG ZHAO

Abstract

Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closed-form formula for cap prices. We show that although a three-factor stochastic volatility model can price at-the-money caps well, significant negative jumps in interest rates are needed to capture the smile. The volatility smile contains information that is not available using only at-the-money caps, and this information is important for understanding term structure models. Copyright 2007 by The American Finance Association.

Suggested Citation

  • Robert Jarrow & Haitao Li & Feng Zhao, 2007. "Interest Rate Caps "Smile" Too! But Can the LIBOR Market Models Capture the Smile?," Journal of Finance, American Finance Association, vol. 62(1), pages 345-382, February.
  • Handle: RePEc:bla:jfinan:v:62:y:2007:i:1:p:345-382
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    Citations

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    Cited by:

    1. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.
    2. Kwai S. Leung & Hon Y. Ng & Hoi Y. Wong, 2014. "Stochastic Skew in the Interest Rate Cap Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1146-1169, December.
    3. R. López & E. Navarro, 2013. "Interest rate and stock return volatility indices for the Eurozone. Investors' gauges of fear during the recent financial crisis," Applied Financial Economics, Taylor & Francis Journals, vol. 23(18), pages 1419-1432, September.
    4. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    5. TAKAMIZAWA, Hideyuki, 2017. "A Term Structure Model of Interest Rates with Quadratic Volatility," Working Paper Series G-1-18, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.
    6. 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.
    7. Cathy Chen & I-Doun Kuo, 2014. "Investor sentiment and interest rate volatility smile: evidence from Eurodollar options markets," Review of Quantitative Finance and Accounting, Springer, vol. 43(2), pages 367-391, August.
    8. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    9. I.-Doun Kuo, 2011. "Pricing and hedging volatility smile under multifactor interest rate models," Review of Quantitative Finance and Accounting, Springer, vol. 36(1), pages 83-104, January.
    10. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2016. "Explaining the volatility smile: non-parametric versus parametric option models," Review of Quantitative Finance and Accounting, Springer, vol. 46(4), pages 907-935, May.
    11. Massimo Costabile & Ivar Massabó & Emilio Russo, 2013. "A Path-Independent Humped Volatility Model for Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 191-210, July.
    12. Haitao Li & Feng Zhao, 2009. "Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4335-4376, November.
    13. Takamizawa, Hideyuki, 2015. "Impact of No-arbitrage on Interest Rate Dynamics," Working Paper Series G-1-5, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.
    14. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.
    15. Leippold, Markus & Strømberg, Jacob, 2014. "Time-changed Lévy LIBOR market model: Pricing and joint estimation of the cap surface and swaption cube," Journal of Financial Economics, Elsevier, vol. 111(1), pages 224-250.

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