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An Empirical Examination of the Convexity Bias in the Pricing of Interest Rate Swaps

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Author Info
Marti G. Subrahmanyam
Anurag Gupta

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Abstract

This paper examines the convexity bias introduced by pricing interest rate swaps off the Eurocurrency futures curve and the incorporation of this bias in prices over time. The convexity bias arises because of the difference between a futures versus a forward contract on interest rates, since the payoff to the latter is non-linear in interest rates. Using daily data from 1987-1996, the differences between market swap rates and the swap rates implied from Eurocurrency futures prices are studied for the four major interest rate swaps markets - $, ',', and DM - and implied rates cannot be explained by default risk differences, term structure effects, liquidity differences or information asymmetries between the swaps and the futures markets. Using a calibrated term structure model, the theoretical value of the convexity bias is found to be comparable to the empirically observed spread. This is evidence of mispricing of swap rates during the earlier years of the study, with a gradual elimination of that mispricing by incorporation of a convexity adjustment in swap pricing over time.

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Publisher Info
Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 98-068.

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Date of creation: Apr 1998
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Handle: RePEc:fth:nystfi:98-068

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Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Web page: http://w4.stern.nyu.edu/finance/
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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. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January. [Downloadable!] (restricted)
  2. French, Kenneth R., 1983. "A comparison of futures and forward prices," Journal of Financial Economics, Elsevier, vol. 12(3), pages 311-342, November. [Downloadable!] (restricted)
  3. Cooper, Ian A & Mello, Antonio S, 1991. " The Default Risk of Swaps," Journal of Finance, American Finance Association, vol. 46(2), pages 597-620, June. [Downloadable!] (restricted)
  4. Minton, Bernadette A., 1997. "An empirical examination of basic valuation models for plain vanilla U.S. interest rate swaps," Journal of Financial Economics, Elsevier, vol. 44(2), pages 251-277, May. [Downloadable!] (restricted)
  5. Jarrow, Robert A. & Oldfield, George S., 1981. "Forward contracts and futures contracts," Journal of Financial Economics, Elsevier, vol. 9(4), pages 373-382, December. [Downloadable!] (restricted)
  6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  7. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December. [Downloadable!]
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)
  11. Meulbroek, Lisa, 1992. " A Comparison of Forward and Futures Prices of an Interest Rate-Sensitive Financial Asset," Journal of Finance, American Finance Association, vol. 47(1), pages 381-96, March. [Downloadable!] (restricted)
  12. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December. [Downloadable!] (restricted)
  13. Richard, Scott F. & Sundaresan, M., 1981. "A continuous time equilibrium model of forward prices and futures prices in a multigood economy," Journal of Financial Economics, Elsevier, vol. 9(4), pages 347-371, December. [Downloadable!] (restricted)
  14. Grinblatt, Mark & Jegadeesh, Narasimhan, 1996. " Relative Pricing of Eurodollar Features and Forward Contracts," Journal of Finance, American Finance Association, vol. 51(4), pages 1499-1522, September. [Downloadable!] (restricted)
  15. Elton, Edwin J & Gruber, Martin J & Rentzler, Joel, 1984. "Intra-Day Tests of the Efficiency of the Treasury Bill Futures Market," The Review of Economics and Statistics, MIT Press, vol. 66(1), pages 129-37, February. [Downloadable!] (restricted)
  16. Sun, Tong-sheng & Sundaresan, Suresh & Wang, Ching, 1993. "Interest rate swaps: An empirical investigation," Journal of Financial Economics, Elsevier, vol. 34(1), pages 77-99, August. [Downloadable!] (restricted)
  17. Litzenberger, Robert H, 1992. " Swaps: Plain and Fanciful," Journal of Finance, American Finance Association, vol. 47(3), pages 831-50, July. [Downloadable!] (restricted)
  18. Rendleman, Richard J, Jr & Carabini, Christopher E, 1979. "The Efficiency of the Treasury Bill Futures Market," Journal of Finance, American Finance Association, vol. 34(4), pages 895-914, September. [Downloadable!] (restricted)
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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. Kim, Don H. & Orphanides, Athanasios, 2005. "Term Structure Estimation with Survey Data on Interest Rate Forecasts," CEPR Discussion Papers 5341, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  2. Sandra Peterson & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "The Valuation of American-Style Swaptions in a Two-factor Spot-Futures Model," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-078, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  3. Marti G. Subrahmanyam & Young Ho Eom & Jun Uno, 2000. "Credit Risk and the Pricing of Japanese Yen Interest Rate Swaps," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-069, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  4. Antulio N. Bomfim, 2003. "Counterparty credit risk in interest rate swaps during times of market stress," Finance and Economics Discussion Series 2003-09, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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