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Estimation of affine term structure models with spanned or unspanned stochastic volatility

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  • Creal, Drew D.
  • Wu, Jing Cynthia

Abstract

We develop new procedures for maximum likelihood estimation of affine term structure models with spanned or unspanned stochastic volatility. Our approach uses linear regression to reduce the dimension of the numerical optimization problem yet it produces the same estimator as maximizing the likelihood. It improves the numerical behavior of estimation by eliminating parameters from the objective function that cause problems for conventional methods. We find that spanned models capture the cross-section of yields well but not volatility while unspanned models fit volatility at the expense of fitting the cross-section.

Suggested Citation

  • Creal, Drew D. & Wu, Jing Cynthia, 2015. "Estimation of affine term structure models with spanned or unspanned stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 60-81.
    • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:60-81
    DOI: 10.1016/j.jeconom.2014.10.003
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    1. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    2. Godsill, Simon J. & Doucet, Arnaud & West, Mike, 2004. "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 156-168, January.
    3. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    4. Francis X. Diebold & Glenn D. Rudebusch, 2012. "Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach," Economics Books, Princeton University Press, edition 1, volume 1, number 9895.
    5. 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.
    6. Duffee, Gregory R., 2013. "Bond Pricing and the Macroeconomy," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 907-967, Elsevier.
    7. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
    8. Christian Gourieroux & Alain Monfort & Vassilis Polimenis, 2002. "Affine Term Structure Models," Working Papers 2002-49, Center for Research in Economics and Statistics.
    9. 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..
    10. Antonio Diez de Los Rios, 2015. "A New Linear Estimator for Gaussian Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 282-295, April.
    11. Michael D. Bauer & Glenn D. Rudebusch & Jing Cynthia Wu, 2012. "Correcting Estimation Bias in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 454-467, April.
    12. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    13. Refet S. Gürkaynak & Jonathan H. Wright, 2012. "Macroeconomics and the Term Structure," Journal of Economic Literature, American Economic Association, vol. 50(2), pages 331-367, June.
    14. 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.
    15. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    16. Pierre Collin‐Dufresne & Robert S. Goldstein & Christopher S. Jones, 2008. "Identification of Maximal Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 63(2), pages 743-795, April.
    17. 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(1), pages 241-272, February.
    18. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2013. "Pricing the term structure with linear regressions," Journal of Financial Economics, Elsevier, vol. 110(1), pages 110-138.
    19. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    20. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    21. Hamilton, James D. & Wu, Jing Cynthia, 2012. "Identification and estimation of Gaussian affine term structure models," Journal of Econometrics, Elsevier, vol. 168(2), pages 315-331.
    22. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    23. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    24. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    25. Anh Le & Kenneth J. Singleton & Qiang Dai, 2010. "Discrete-Time Affine-super-ℚ Term Structure Models with Generalized Market Prices of Risk," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2184-2227.
    26. Haitao Li & Feng Zhao, 2006. "Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives," Journal of Finance, American Finance Association, vol. 61(1), pages 341-378, February.
    27. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    28. Malik, Sheheryar & Pitt, Michael K., 2011. "Particle filters for continuous likelihood evaluation and maximisation," Journal of Econometrics, Elsevier, vol. 165(2), pages 190-209.
    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. Hamilton, James D. & Wu, Jing Cynthia, 2014. "Testable implications of affine term structure models," Journal of Econometrics, Elsevier, vol. 178(P2), pages 231-242.
    31. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    32. Aït-Sahalia, Yacine & Kimmel, Robert L., 2010. "Estimating affine multifactor term structure models using closed-form likelihood expansions," Journal of Financial Economics, Elsevier, vol. 98(1), pages 113-144, October.
    33. Don H. Kim & Jonathan H. Wright, 2005. "An arbitrage-free three-factor term structure model and the recent behavior of long-term yields and distant-horizon forward rates," Finance and Economics Discussion Series 2005-33, Board of Governors of the Federal Reserve System (U.S.).
    34. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    35. 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, February.
    36. 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.
    37. Gregory R. Duffee, 2011. "Information in (and not in) the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 24(9), pages 2895-2934.
    38. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    39. 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.
    40. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    41. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    42. Jacquier, Eric & Johannes, Michael & Polson, Nicholas, 2007. "MCMC maximum likelihood for latent state models," Journal of Econometrics, Elsevier, vol. 137(2), pages 615-640, April.
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    Cited by:

    1. Drew D. Creal & Jing Cynthia Wu, 2020. "Bond risk premia in consumption‐based models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1461-1484, November.
    2. P. Byrne, Joseph & Cao, Shuo & Korobilis, Dimitris, 2015. "Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty," SIRE Discussion Papers 2015-71, Scottish Institute for Research in Economics (SIRE).
    3. Jing Cynthia Wu & Fan Dora Xia, 2016. "Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(2-3), pages 253-291, March.
    4. Hitesh Doshi & Kris Jacobs & Rui Liu, 2021. "Information in the Term Structure: A Forecasting Perspective," Management Science, INFORMS, vol. 67(8), pages 5255-5277, August.
    5. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2021. "No‐arbitrage priors, drifting volatilities, and the term structure of interest rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 495-516, August.
    6. Hlouskova, Jaroslava & Sögner, Leopold, 2020. "GMM estimation of affine term structure models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 2-15.
    7. Drew D. Creal & Jing Cynthia Wu, 2017. "Monetary Policy Uncertainty And Economic Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1317-1354, November.
    8. Liu, Yan & Wu, Jing Cynthia, 2021. "Reconstructing the yield curve," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1395-1425.
    9. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    10. Michael D. Bauer, 2018. "Restrictions on Risk Prices in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 196-211, April.
    11. Rangan Gupta & Hylton Hollander & Rudi Steinbach, 2020. "Forecasting output growth using a DSGE-based decomposition of the South African yield curve," Empirical Economics, Springer, vol. 58(1), pages 351-378, January.
    12. Jing Cynthia Wu & Fan Dora Xia, 2020. "Negative interest rate policy and the yield curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 653-672, September.
    13. Han, Yang & Jiao, Anqi & Ma, Jun, 2021. "The predictive power of Nelson–Siegel factor loadings for the real economy," Journal of Empirical Finance, Elsevier, vol. 64(C), pages 95-127.
    14. Stefano Giglio & Bryan Kelly, 2018. "Excess Volatility: Beyond Discount Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 71-127.
    15. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    16. Januj Amar Juneja, 2021. "How do invariant transformations affect the calibration and optimization of the Kalman filtering algorithm used in the estimation of continuous-time affine term structure models?," Computational Management Science, Springer, vol. 18(1), pages 73-97, January.
    17. 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.
    18. Anne Lundgaard Hansen, 2018. "Volatility-Induced Stationarity and Error-Correction in Macro-Finance Term Structure Modeling," Discussion Papers 18-12, University of Copenhagen. Department of Economics.
    19. Hansen, Anne Lundgaard, 2021. "Modeling persistent interest rates with double-autoregressive processes," Journal of Banking & Finance, Elsevier, vol. 133(C).
    20. Januj Amar Juneja, 2022. "A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 173-220, June.
    21. P. Byrne, Joseph & Cao, Shuo & Korobilis, Dimitris, 2015. "Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-71, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    22. Gordon H. Dash & Nina Kajiji & Domenic Vonella, 2018. "The role of supervised learning in the decision process to fair trade US municipal debt," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 139-168, June.
    23. Peter Feldhütter, 2016. "Can Affine Models Match the Moments in Bond Yields?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-56, June.
    24. Gideon Magnus, 2016. "A plausible model of yield curve dynamics," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 30(2), pages 205-228, May.
    25. Leandro Maciel & Fernando Gomide & Rosangela Ballini, 2016. "Evolving Fuzzy-GARCH Approach for Financial Volatility Modeling and Forecasting," Computational Economics, Springer;Society for Computational Economics, vol. 48(3), pages 379-398, October.

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    More about this item

    Keywords

    Affine term structure models; Unspanned stochastic volatility; Estimation;
    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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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