Advanced Search
MyIDEAS: Login to save this paper or follow this series

Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification test for Affine Term Structure Models

Contents:

Author Info

  • Torben G. Andersen
  • Luca Benzoni

Abstract

We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most 'affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds ("realized yield volatility") through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, Gaussian-quadratic and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.nber.org/papers/w12962.pdf
Download Restriction: no

Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12962.

as in new window
Length:
Date of creation: Mar 2007
Date of revision:
Publication status: published as Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, 04.
Handle: RePEc:nbr:nberwo:12962

Note: AP
Contact details of provider:
Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
Phone: 617-868-3900
Email:
Web page: http://www.nber.org
More information through EDIRC

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
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.:
as in new window
  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2007. "Real-Time Price Discovery in Global Stock, Bond and Foreign Exchange Markets," CREATES Research Papers 2007-20, School of Economics and Management, University of Aarhus.
  2. Olivier Scaillet., 2003. "Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility," THEMA Working Papers 2003-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  3. Ait-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2005. "Ultra high frequency volatility estimation with dependent microstructure noise," Discussion Paper Series 1: Economic Studies 2005,30, Deutsche Bundesbank, Research Centre.
  4. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  6. Torben G. Andersen & Tim Bollerslev, 1998. "Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies," Journal of Finance, American Finance Association, vol. 53(1), pages 219-265, 02.
  7. Michael J. Fleming & Eli M. Remolona, 1997. "What moves the bond market?," Research Paper 9706, Federal Reserve Bank of New York.
  8. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
  9. Michael J. Fleming & Eli M. Remolona, 1999. "Price Formation and Liquidity in the U.S. Treasury Market: The Response to Public Information," Journal of Finance, American Finance Association, vol. 54(5), pages 1901-1915, October.
  10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2003. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange," American Economic Review, American Economic Association, vol. 93(1), pages 38-62, March.
  11. Andrew Ang & Monika Piazzesi & Min Wei, 2003. "What does the yield curve tell us about GDP growth?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  12. Engle, Robert F, 1998. "Macroeconomic Announcements and Volatility of Treasury Futures," University of California at San Diego, Economics Working Paper Series qt7rd4g3bk, Department of Economics, UC San Diego.
  13. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," Working papers 353, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-30, June.
  15. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  16. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
  17. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
  18. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
  19. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
  20. Pierre Collin-Dufresne & Christopher S. Jones & Robert S. Goldstein, 2004. "Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility," NBER Working Papers 10756, National Bureau of Economic Research, Inc.
  21. Diebold, Francis X. & Piazzesi, Monica & Rudebusch, Glenn D., 2005. "Modeling bond yields in finance and macroeconomics," CFS Working Paper Series 2005/03, Center for Financial Studies (CFS).
  22. Duffee, Gregory R, 1996. " Idiosyncratic Variation of Treasury Bill Yields," Journal of Finance, American Finance Association, vol. 51(2), pages 527-51, June.
  23. Diebold, Francis X. & Li, Canlin, 2003. "Forecasting the term structure of government bond yields," CFS Working Paper Series 2004/09, Center for Financial Studies (CFS).
  24. Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, 08.
  25. Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc.
  26. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  27. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
  28. Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," Economics Series Working Papers 2004-FE-20, University of Oxford, Department of Economics.
  29. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
  30. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
  31. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  32. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2001. "An Empirical Investigation of Continuous-Time Equity Return Models," NBER Working Papers 8510, National Bureau of Economic Research, Inc.
  33. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  34. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
  35. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  36. Qiang Dai & Thomas Philippon, 2005. "Fiscal Policy and the Term Structure of Interest Rates," NBER Working Papers 11574, National Bureau of Economic Research, Inc.
  37. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  38. Andersen, Torben G, 2000. "Some Reflections on Analysis of High-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 146-53, April.
  39. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
  40. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  41. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
  42. G. William Schwert, 1990. "Stock Volatility and the Crash of '87," NBER Working Papers 2954, National Bureau of Economic Research, Inc.
  43. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
  44. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2005. "Real-Time Price Discovery in Stock, Bond and Foreign Exchange Markets," NBER Working Papers 11312, National Bureau of Economic Research, Inc.
  45. Balduzzi, Pierluigi & Elton, Edwin J. & Green, T. Clifton, 2001. "Economic News and Bond Prices: Evidence from the U.S. Treasury Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(04), pages 523-543, December.
  46. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
  47. Ruslan Bikbov & Mikhail Chernov, 2010. "No-arbitrage macroeconomic determinants of the yield curve," Post-Print peer-00732517, HAL.
  48. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, 01.
  49. Daniel F. Waggoner, 1997. "Spline methods for extracting interest rate curves from coupon bond prices," Working Paper 97-10, Federal Reserve Bank of Atlanta.
  50. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  51. Michael W. Brandt & Kenneth A. Kavajecz, 2004. "Price Discovery in the U.S. Treasury Market: The Impact of Orderflow and Liquidity on the Yield Curve," Journal of Finance, American Finance Association, vol. 59(6), pages 2623-2654, December.
  52. Paolo Pasquariello & Clara Vega, 2006. "Informed and strategic order flow in the bond markets," International Finance Discussion Papers 874, Board of Governors of the Federal Reserve System (U.S.).
  53. Pierluigi Balduzzi & Edwin J. Elton & T. Clifton Green, 1996. "Economic News and the Yield Curve: Evidence From the U.S. Treasury Market," New York University, Leonard N. Stern School Finance Department Working Paper Seires 96-13, New York University, Leonard N. Stern School of Business-.
  54. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
  55. T. Clifton Green, 2004. "Economic News and the Impact of Trading on Bond Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1201-1234, 06.
  56. Ahn, Dong-Hyun & Dittmar, Robert F. & Gallant, A. Ronald & Gao, Bin, 2003. "Purebred or hybrid?: Reproducing the volatility in term structure dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 147-180.
  57. Michael J. Fleming, 1997. "The round-the-clock market for U.S. Treasury securities," Economic Policy Review, Federal Reserve Bank of New York, issue Jul, pages 9-32.
  58. Michael J. Fleming, 2001. "Measuring treasury market liquidity," Staff Reports 133, Federal Reserve Bank of New York.
  59. Michael J. Fleming & Kenneth D. Garbade, 2002. "When the back office moved to the front burner: settlement fails in the treasury market after 9/11," Economic Policy Review, Federal Reserve Bank of New York, issue Nov, pages 35-57.
  60. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
  61. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  62. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  63. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  64. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
  65. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  66. Mark Fisher & Douglas Nychka & David Zervos, 1995. "Fitting the term structure of interest rates with smoothing splines," Finance and Economics Discussion Series 95-1, Board of Governors of the Federal Reserve System (U.S.).
  67. Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Xavier Gabaix, 2007. "Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices," NBER Working Papers 13430, National Bureau of Economic Research, Inc.
  2. Gürkaynak, Refet S. & Wright, Jonathan, 2010. "Macroeconomics and the Term Structure," CEPR Discussion Papers 8018, C.E.P.R. Discussion Papers.
  3. Jens H.E. Christensen, 2013. "A regime-switching model of the yield curve at the zero bound," Working Paper Series 2013-34, Federal Reserve Bank of San Francisco.
  4. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
  5. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Cahiers de recherche 1404, CIRPEE.
  6. Christensen, Jens H.E. & Rudebusch, Glenn D., 2013. "Modeling yields at the zero lower bound: are shadow rates the solution?," Working Paper Series 2013-39, Federal Reserve Bank of San Francisco.
  7. Juneja, Januj, 2014. "Term structure estimation in the presence of autocorrelation," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 119-129.
  8. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements.
  9. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2014. "Can spanned term structure factors drive stochastic yield volatility?," Working Paper Series 2014-3, Federal Reserve Bank of San Francisco.
  10. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:12962. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.