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Libor and Swap Market Models for the Pricing of Interest Rate Derivatives: An Empirical Analysis

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  • Jong, F.C.J.M. de
  • Driessen, J.J.A.G.
  • Pelsser, A.

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek, and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions.A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices.For both one-factor and two-factor models we analyze how well they price caplets and swaptions that were not used for calibration.We show that the Libor Market Models in general lead to better prediction of derivative prices that were not used for calibration than the Swap Market Models.A one-factor Libor Market Model that exhibits mean-reversion gives a good fit of the derivative prices, and adding a second factor only decreases pricing errors to a small extent.We also find that models that are chosen to exactly match certain derivative prices are overfitted. Finally, a regression analysis reveals that the pricing errors are correlated with the shape of the term structure of interest rates.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2000-35.

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Date of creation: 2000
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Handle: RePEc:dgr:kubcen:200035

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Related research

Keywords: Term Structure Models; Interest Rate Derivatives; Lognormal Pricing Models; Black Formula;

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References

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  1. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August.
  2. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
  3. Geert Bekaert & Robert J. Hodrick & David A. Marshall, 1996. "On Biases in Tests of the Expecations Hypothesis of the Term Structure Of Interest Rates," NBER Technical Working Papers 0191, National Bureau of Economic Research, Inc.
  4. 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.
  5. Xiaoliang Zhao & Paul Glasserman, 2000. "Arbitrage-free discretization of lognormal forward Libor and swap rate models," Finance and Stochastics, Springer, vol. 4(1), pages 35-68.
  6. Alan Brace & Dariusz G�atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
  7. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  8. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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  13. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
  14. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  15. Flesaker, Bjorn, 1993. "Testing the Heath-Jarrow-Morton/Ho-Lee Model of Interest Rate Contingent Claims Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 483-495, December.
  16. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  17. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
  18. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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Citations

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Cited by:
  1. Riccardo Rebonato, 2006. "Forward-Rate Volatilities And The Swaption Matrix: Why Neither Time-Homogeneity Nor Time-Dependence Are Enough," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 705-746.
  2. Jong, F.C.J.M. de & Driessen, J. & Pelsser, A., 2004. "On the information in the interest rate term structure and option prices," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3159390, Tilburg University.
  3. S.Galluccio & Z. Huang & J.-M. Ly & O. Scaillet, 2005. "Theory and Calibration of Swap Market Models," FAME Research Paper Series rp107, International Center for Financial Asset Management and Engineering.
  4. Mireille Bossy & Rajna Gibson & Francois-Serge Lhabitant & Nathalie Pistre & Denis Talay, 2006. "Model misspecification analysis for bond options and Markovian hedging strategies," Review of Derivatives Research, Springer, vol. 9(2), pages 109-135, September.
  5. Mihaela Tuca, 2009. "Calibration of LIBOR Market Model: Comparison between the Separated and the Approximate Approach," Advances in Economic and Financial Research - DOFIN Working Paper Series 27, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
  6. Christian Zühlsdorff, 2002. "Extended Libor Market Models with Affine and Quadratic Volatility," Bonn Econ Discussion Papers bgse6_2002, University of Bonn, Germany.
  7. Carol Alexandra, 2002. "Common Correlation and Calibrating the Lognormal Forward Rate Model," ICMA Centre Discussion Papers in Finance icma-dp2002-18, Henley Business School, Reading University, revised Jan 2003.

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