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

  • Anurag Gupta
  • Marti G. Subrahmanyam

This paper examines the convexity bias introduced by pricing interest rate swaps off the Eurocurrency futures curve and the market's adjustment of this bias in prices over time. The convexity bias arises because of the difference between a futures contract and 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 swap markets - $, £, DM and ¥. The evidence suggests that swaps were being priced off the futures curve (i.e. by ignoring the convexity adjustment) during the earlier years of the study, after which the market swap rates drifted below the rates implied by futures prices. The empirical analysis shows that this spread between the market and futures-implied swap rates cannot be explained by default risk differences, liquidity differences or information asymmetries between the swap and the futures markets. Using alternative term structure models (one-factor Vasicek, Cox-Ingersoll and Ross, Hull and White, Black and Karasinski, and the two-factor Heath, Jarrow and Morton), the theoretical value of the convexity bias is found to be related to the empirically observed swap-futures differential. We interpret these results as evidence of mispricing of swap contracts 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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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 99-001.

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Date of creation: Feb 1999
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Handle: RePEc:fth:nystfi:99-001
Contact details of provider: 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
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/

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  1. 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.
  2. 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.
  3. 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.
  4. French, Kenneth R., 1983. "A comparison of futures and forward prices," Journal of Financial Economics, Elsevier, vol. 12(3), pages 311-342, November.
  5. 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.
  6. 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.
  7. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
  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.
  9. Avraham Kamara, 1988. "Market Trading Structures and Asset Pricing: Evidence from the Treasury- Bill Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 357-375.
  10. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  12. Sundaresan, Suresh, 1991. "Futures Prices on Yields, Forward Prices, and Implied Forward Prices from Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 409-424, September.
  13. Kamara, A., 1988. "Trading Structures And Asset Pricing: Evidence From The Treasury Bill Markets," Papers 169, Columbia - Center for Futures Markets.
  14. 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.
  15. 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.
  16. Litzenberger, Robert H, 1992. " Swaps: Plain and Fanciful," Journal of Finance, American Finance Association, vol. 47(3), pages 831-50, July.
  17. Jarrow, Robert A. & Oldfield, George S., 1981. "Forward contracts and futures contracts," Journal of Financial Economics, Elsevier, vol. 9(4), pages 373-382, December.
  18. Robert W. Kolb & Gerald D. Gay, 1985. "A Pricing Anomaly In Treasury Bill Futures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 8(2), pages 157-167, 06.
  19. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-49, July.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  25. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
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