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An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices

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Author Info
Ravi Jagannathan
Andrew Kaplin
Steve Guoqiang Sun

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Abstract

We evaluate the classical Cox, Ingersoll and Ross (1985) (CIR) model using data on LIBOR, swap rates and caps and swaptions. With three factors the CIR model is able to fit the term structure of LIBOR and swap rates rather well. The model is able to match the hump shaped unconditional term structure of volatility in the LIBOR-swap market. However, statistical tests indicate that the model is misspecified. In particular the pricing errors are related to the slope of the swap yield curve. The economic importance of these shortcomings is highlighted when the model is confronted with data on cap and swaption prices. Pricing errors are large relative to the bid-ask spread in these markets. The model tends to overvalue shorter maturity caps and undervalue longer maturity caps. With only one or two factors, the model also tends to undervalue swaptions. Our findings point out the need for evaluating term structure models using data on derivative prices.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 8682.

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Date of creation: Dec 2001
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Handle: RePEc:nbr:nberwo:8682

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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Cited by:
(explanations, 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.)

  1. Hao Zhou, 2001. "Jump-diffusion term structure and Ito conditional moment generator," Finance and Economics Discussion Series 2001-28, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  5. 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. [Downloadable!]
  6. Clarida, Richard & Sarno, Lucio & Taylor, Mark P & Valente, Giorgio, 2005. "The Role of Asymmetries and Regime Shifts in the Term Structure of Interest Rates," CEPR Discussion Papers 4835, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  7. Don H. Kim & Athanasios Orphanides, 2005. "Term structure estimation with survey data on interest rate forecasts," Finance and Economics Discussion Series 2005-48, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  8. Duarte, Jefferson., 2003. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Finance Lab Working Papers flwp_49, Finance Lab, Ibmec São Paulo. [Downloadable!]
  9. Jin-Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities," Working Paper 0619, Federal Reserve Bank of Cleveland. [Downloadable!]
  10. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena. [Downloadable!]
  11. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements. [Downloadable!]
  12. Della Corte, Pasquale & Sarno, Lucio & Thornton, Daniel L, 2007. "The Expectation Hypothesis of the Term Structure of Very Short-Term Rates: Statistical Tests and Economic Value," CEPR Discussion Papers 6445, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  13. Massoud Heidari & Liuren Wu, 2002. "Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rates and Interest Rate Derivatives," Finance 0207010, EconWPA, revised 05 Sep 2002. [Downloadable!]
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