IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v171y2025ics0378426624002681.html
   My bibliography  Save this article

Unspanned stochastic volatility in the linear-rational square-root model: Evidence from the Treasury market

Author

Listed:
  • Hansen, Jorge Wolfgang

Abstract

This study examines the ability of the linear-rational square-root model to simultaneously capture cross-sectional and time-series dynamics of bond yields and their variances. The preferred model specification comprises five factors, two of which are not spanned by the yield curve, introducing unspanned stochastic volatility (USV). This specification provides a close in-sample fit to yields and yield variances, emphasizing the need for USV. Out-of-sample testing demonstrates low variance forecast errors. The specification provides evidence of USV in conditional yield variance and bond risk premia, linked to macroeconomic uncertainty.

Suggested Citation

  • Hansen, Jorge Wolfgang, 2025. "Unspanned stochastic volatility in the linear-rational square-root model: Evidence from the Treasury market," Journal of Banking & Finance, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:jbfina:v:171:y:2025:i:c:s0378426624002681
    DOI: 10.1016/j.jbankfin.2024.107354
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426624002681
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2024.107354?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
    2. 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, January.
    3. Duffee, Gregory R, 1996. "Idiosyncratic Variation of Treasury Bill Yields," Journal of Finance, American Finance Association, vol. 51(2), pages 527-551, June.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Robin Greenwood & Dimitri Vayanos, 2014. "Bond Supply and Excess Bond Returns," The Review of Financial Studies, Society for Financial Studies, vol. 27(3), pages 663-713.
    6. Scott Joslin & Marcel Priebsch & Kenneth J. Singleton, 2014. "Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks," Journal of Finance, American Finance Association, vol. 69(3), pages 1197-1233, June.
    7. Jacobs, Kris & Karoui, Lotfi, 2009. "Conditional volatility in affine term-structure models: Evidence from Treasury and swap markets," Journal of Financial Economics, Elsevier, vol. 91(3), pages 288-318, March.
    8. Gurkaynak, Refet S. & Sack, Brian & Wright, Jonathan H., 2007. "The U.S. Treasury yield curve: 1961 to the present," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2291-2304, November.
    9. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2021. "Macro risks and the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 141(2), pages 479-504.
    10. Liu, Yan & Wu, Jing Cynthia, 2021. "Reconstructing the yield curve," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1395-1425.
    11. 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.
    12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    13. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
    14. Scott Joslin, 2018. "Can Unspanned Stochastic Volatility Models Explain the Cross Section of Bond Volatilities?," Management Science, INFORMS, vol. 64(4), pages 1707-1726, April.
    15. John Y. Campbell & Robert J. Shiller, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 495-514.
    16. Anna Cieslak & Pavol Povala, 2016. "Information in the Term Structure of Yield Curve Volatility," Journal of Finance, American Finance Association, vol. 71(3), pages 1393-1436, June.
    17. Kyle Jurado & Sydney C. Ludvigson & Serena Ng, 2015. "Measuring Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1177-1216, March.
    18. Anna Cieslak & Pavol Povala, 2015. "Expected Returns in Treasury Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2859-2901.
    19. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    20. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    21. Michael D. Bauer & James D. Hamilton, 2018. "Robust Bond Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 399-448.
    22. 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, April.
    23. Eric Ghysels & Casidhe Horan & Emanuel Moench, 2018. "Forecasting through the Rearview Mirror: Data Revisions and Bond Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 678-714.
    24. Geert Bekaert & Eric C. Engstrom & Nancy R. Xu, 2022. "The Time Variation in Risk Appetite and Uncertainty," Management Science, INFORMS, vol. 68(6), pages 3975-4004, June.
    25. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    26. Samuel Thompson, 2008. "Identifying Term Structure Volatility from the LIBOR-Swap Curve," The Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 819-854, April.
    27. Ravi Bansal & Ivan Shaliastovich, 2013. "A Long-Run Risks Explanation of Predictability Puzzles in Bond and Currency Markets," The Review of Financial Studies, Society for Financial Studies, vol. 26(1), pages 1-33.
    28. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    29. Joslin, Scott & Konchitchki, Yaniv, 2018. "Interest rate volatility, the yield curve, and the macroeconomy," Journal of Financial Economics, Elsevier, vol. 128(2), pages 344-362.
    30. Ilan Cooper, 2009. "Time-Varying Risk Premiums and the Output Gap," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2601-2633, July.
    31. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    32. Jonathan H. Wright, 2011. "Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset," American Economic Review, American Economic Association, vol. 101(4), pages 1514-1534, June.
    33. 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, August.
    34. Joslin, Scott & Le, Anh & Singleton, Kenneth J., 2013. "Why Gaussian macro-finance term structure models are (nearly) unconstrained factor-VARs," Journal of Financial Economics, Elsevier, vol. 109(3), pages 604-622.
    35. Martin Møller Andreasen & Kasper Jørgensen & Andrew Meldrum, 2019. "Bond Risk Premiums at the Zero Lower Bound," CREATES Research Papers 2019-10, Department of Economics and Business Economics, Aarhus University.
    36. David S. Bates, 2006. "Maximum Likelihood Estimation of Latent Affine Processes," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 909-965.
    37. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    38. Martin M. Andreasen & Kasper Joergensen & Andrew C. Meldrum, 2019. "Bond Risk Premiums at the Zero Lower Bound," Finance and Economics Discussion Series 2019-040, Board of Governors of the Federal Reserve System (U.S.).
    39. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.
    40. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    41. Gregory R. Duffee, 2011. "Information in (and not in) the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 24(9), pages 2895-2934.
    42. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-692, September.
    43. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Junye & Sarno, Lucio & Zinna, Gabriele, 2024. "Risks and risk premia in the US Treasury market," Journal of Economic Dynamics and Control, Elsevier, vol. 158(C).
    2. Christensen, Bent Jesper & Kjær, Mads Markvart & Veliyev, Bezirgen, 2023. "The incremental information in the yield curve about future interest rate risk," Journal of Banking & Finance, Elsevier, vol. 155(C).
    3. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    4. Daniel Borup & Jonas N. Eriksen & Mads M. Kjær & Martin Thyrsgaard, 2024. "Predicting Bond Return Predictability," Management Science, INFORMS, vol. 70(2), pages 931-951, February.
    5. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2021. "Macro risks and the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 141(2), pages 479-504.
    6. Hansen, Anne Lundgaard, 2024. "Time-varying variance decomposition of macro-finance term structure models," Journal of Empirical Finance, Elsevier, vol. 79(C).
    7. Jing-Zhi Huang & Zhan Shi, 2023. "Machine-Learning-Based Return Predictors and the Spanning Controversy in Macro-Finance," Management Science, INFORMS, vol. 69(3), pages 1780-1804, March.
    8. Peter Carr & Liuren Wu, 2023. "Decomposing Long Bond Returns: A Decentralized Theory," Review of Finance, European Finance Association, vol. 27(3), pages 997-1026.
    9. Bakshi, Gurdip & Crosby, John & Gao, Xiaohui & Hansen, Jorge W., 2023. "Treasury option returns and models with unspanned risks," Journal of Financial Economics, Elsevier, vol. 150(3).
    10. Doshi, Hitesh & Jacobs, Kris & Liu, Rui, 2018. "Macroeconomic determinants of the term structure: Long-run and short-run dynamics," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 99-122.
    11. Chiarella, Carl & Hsiao, Chih-Ying & Tô, Thuy-Duong, 2016. "Stochastic correlation and risk premia in term structure models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 59-78.
    12. Guo, Bin & Huang, Fuzhe & Li, Kai, 2022. "Time to build and bond risk premia," Journal of Economic Dynamics and Control, Elsevier, vol. 136(C).
    13. Hansen, Anne Lundgaard, 2021. "Modeling persistent interest rates with double-autoregressive processes," Journal of Banking & Finance, Elsevier, vol. 133(C).
    14. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    15. Rui Liu, 2019. "Forecasting Bond Risk Premia with Unspanned Macroeconomic Information," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 1-62, March.
    16. Yung, Julieta, 2021. "Can interest rate factors explain exchange rate fluctuations?," Journal of Empirical Finance, Elsevier, vol. 61(C), pages 34-56.
    17. Christensen, Bent Jesper & van der Wel, Michel, 2019. "An asset pricing approach to testing general term structure models," Journal of Financial Economics, Elsevier, vol. 134(1), pages 165-191.
    18. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    19. Feng Zhao & Guofu Zhou & Xiaoneng Zhu, 2021. "Unspanned Global Macro Risks in Bond Returns," Management Science, INFORMS, vol. 67(12), pages 7825-7843, December.
    20. Michael D. Bauer & Glenn D. Rudebusch, 2020. "Interest Rates under Falling Stars," American Economic Review, American Economic Association, vol. 110(5), pages 1316-1354, May.

    More about this item

    Keywords

    Interest rate model; Treasury market; Unscented Kalman filter; Unspanned stochastic volatility; Unspanned risk premia;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jbfina:v:171:y:2025:i:c:s0378426624002681. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbf .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.