Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?
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
|Date of creation:||11 Aug 2004|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
- Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997.
" Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Journal of Finance,
American Finance Association, vol. 52(1), pages 409-30, March.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
- Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
- Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
- Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-84.
- Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
- Ravi Jagannathan & Andrew Kaplin & Steve Guoqiang Sun, 2001.
"An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices,"
NBER Working Papers
8682, National Bureau of Economic Research, Inc.
- Jagannathan, Ravi & Kaplin, Andrew & Sun, Steve, 2003. "An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and swaption prices," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 113-146.
- Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
- Santa-Clara, Pedro & Sornette, Didier, 2001.
"The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks,"
Review of Financial Studies,
Society for Financial Studies, vol. 14(1), pages 149-85.
- P. Santa-Clara & D. Sornette, 1998. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Papers cond-mat/9801321, arXiv.org.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992.
"Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,"
Econometric Society, vol. 60(1), pages 77-105, January.
- David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
- Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
- Diebold, Francis X & Mariano, Roberto S, 2002.
"Comparing Predictive Accuracy,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 134-44, January.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
When requesting a correction, please mention this item's handle: RePEc:ecm:nawm04:431. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.