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

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  • Marti G. Subrahmanyam
  • Anurag Gupta

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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  • Marti G. Subrahmanyam & Anurag Gupta, 1998. "An Empirical Examination of the Convexity Bias in the Pricing of Interest Rate Swaps," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-068, New York University, Leonard N. Stern School of Business-.
  • Handle: RePEc:fth:nystfi:98-068
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    Cited by:

    1. 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.
    2. Teo, Melvyn, 2011. "The liquidity risk of liquid hedge funds," Journal of Financial Economics, Elsevier, vol. 100(1), pages 24-44, April.
    3. 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.
    4. 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, April.
    5. repec:wyi:journl:002109 is not listed on IDEAS
    6. Azad, A.S.M. Sohel & Fang, Victor & Hung, Chi-Hsiou, 2012. "Linking the interest rate swap markets to the macroeconomic risk: The UK and us evidence," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 38-47.
    7. Stefania D'Amico & Don H Kim & Min Wei, 2008. "Tips from TIPS: the informational content of Treasury Inflation-Protected Security prices," BIS Working Papers 248, Bank for International Settlements.
    8. Jun Liu & Francis A. Longstaff & Ravit E. Mandell, 2006. "The Market Price of Risk in Interest Rate Swaps: The Roles of Default and Liquidity Risks," The Journal of Business, University of Chicago Press, vol. 79(5), pages 2337-2360, September.
    9. Azad, A.S.M. Sohel & Batten, Jonathan A. & Fang, Victor, 2015. "What determines the yen swap spread?," International Review of Financial Analysis, Elsevier, vol. 40(C), pages 1-13.
    10. 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-.
    11. Nneji, Ogonna, 2015. "Liquidity shocks and stock bubbles," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 35(C), pages 132-146.
    12. Poskitt, Russell, 2006. "Swap pricing: Evidence from the sterling swap market," Global Finance Journal, Elsevier, vol. 17(2), pages 294-308, December.
    13. 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.).
    14. Adam Kobor & Lishan Shi & Ivan Zelenko, 2005. "What Determines U.S. Swap Spreads?," World Bank Publications, The World Bank, number 7272.
    15. Sohel Azad, A.S.M. & Batten, Jonathan A. & Fang, Victor & Wickramanayake, Jayasinghe, 2015. "International swap market contagion and volatility," Economic Modelling, Elsevier, vol. 47(C), pages 355-371.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. Peterson, Sandra & Stapleton, Richard C. & Subrahmanyam, Marti G., 2003. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(04), pages 847-880, December.
    23. 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-.

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