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

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  • Anurag Gupta
  • Marti G. Subrahmanyam

Abstract

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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Bibliographic 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 99-001.

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Date of creation: Feb 1999
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Handle: RePEc:fth:nystfi:99-001

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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
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/
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  1. 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.
  2. 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.
  3. Litzenberger, Robert H, 1992. " Swaps: Plain and Fanciful," Journal of Finance, American Finance Association, vol. 47(3), pages 831-50, July.
  4. 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.
  5. 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.
  6. 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.
  7. French, Kenneth R., 1983. "A comparison of futures and forward prices," Journal of Financial Economics, Elsevier, vol. 12(3), pages 311-342, November.
  8. 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.
  9. 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.
  10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-49, July.
  17. 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.
  18. Jarrow, Robert A. & Oldfield, George S., 1981. "Forward contracts and futures contracts," Journal of Financial Economics, Elsevier, vol. 9(4), pages 373-382, December.
  19. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  20. 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.
  21. 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.
  22. 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. Poskitt, Russell, 2006. "Swap pricing: Evidence from the sterling swap market," Global Finance Journal, Elsevier, vol. 17(2), pages 294-308, December.
  2. Liu, Jun & Longstaff, Francis A. & Mandell, Ravit E., 2000. "The Market Price of Credit Risk: An Empirical Analysis of Interest Rate Swap Spreads," University of California at Los Angeles, Anderson Graduate School of Management qt0zw4f9w6, Anderson Graduate School of Management, UCLA.
  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-.
  4. repec:wyi:journl:002109 is not listed on IDEAS
  5. Gupta, Anurag & Subrahmanyam, Marti G., 2005. "Pricing and hedging interest rate options: Evidence from cap-floor markets," Journal of Banking & Finance, Elsevier, vol. 29(3), pages 701-733, March.
  6. Jyh-Horng Lin & Min-Li Yi, 2005. "Loan Portfolio Swaps and Optimal Lending," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 177-198, January.
  7. Kim, Don H. & Orphanides, Athanasios, 2012. "Term Structure Estimation with Survey Data on Interest Rate Forecasts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(01), pages 241-272, February.
  8. 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-.
  9. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246 Elsevier.
  10. Nicole M. Boyson & Christof W. Stahel & René M. Stulz, 2010. "Hedge Fund Contagion and Liquidity Shocks," Journal of Finance, American Finance Association, vol. 65(5), pages 1789-1816, October.
  11. Stefania D'Amico & Don H. Kim & Min Wei, 2010. "Tips from TIPS: the informational content of Treasury Inflation-Protected Security prices," Finance and Economics Discussion Series 2010-19, Board of Governors of the Federal Reserve System (U.S.).
  12. Boyson, Nicole M. & Stahel, Christof W. & Stulz, Rene M., 2011. "Liquidity Shocks and Hedge Fund Contagion," Working Paper Series 2011-12, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
  13. Jun Liu & Francis A. Longstaff & Ravit E. Mandell, 2002. "The Market Price of Credit Risk: An Empirical Analysis of Interest Rate Swap Spreads," NBER Working Papers 8990, National Bureau of Economic Research, Inc.
  14. Colin Lizieri & Gianluca Marcato & Paul Ogden & Andrew Baum, 2012. "Pricing Inefficiencies in Private Real Estate Markets Using Total Return Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 774-803, October.
  15. Liu, Jun & Longstaff, Francis A. & Mandell, Ravit E., 2004. "The Market Price Of Risk In Interest Rate Swaps: The Roles Of Default And Liquidity Risks," University of California at Los Angeles, Anderson Graduate School of Management qt5z42g22g, Anderson Graduate School of Management, UCLA.
  16. Longstaff, Francis A & Santa-Clara, Pedro & Schwartz, Eduardo S, 2000. "The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence," University of California at Los Angeles, Anderson Graduate School of Management qt65f1914p, Anderson Graduate School of Management, UCLA.
  17. Adam Kobor & Lishan Shi & Ivan Zelenko, 2005. "What Determines U.S. Swap Spreads?," World Bank Publications, The World Bank, number 7272, October.
  18. 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.).

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