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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.

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Bibliographic Info

Article provided by American Finance Association in its journal The Journal of Finance.

Volume (Year): 62 (2007)
Issue (Month): 1 (02)
Pages: 345-382

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Handle: RePEc:bla:jfinan:v:62:y:2007:i:1:p:345-382

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.

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