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Efficient bond price approximations in non-linear equilibrium-based term structure models

Author

Listed:
  • Andreasen Martin M.

    (CCBS, Bank of England and Centre for Macroeconomics, Bank of England, Threadneedle Street, London, EC2R 8AH, UK)

  • Zabczyk Pawel

    (CCBS, Bank of England and Centre for Macroeconomics, Bank of England, Threadneedle Street, London, EC2R 8AH, UK)

Abstract

This paper develops an efficient method to compute higher-order perturbation approximations of bond prices. At third order, our approach can significantly shorten the approximation process and its precision exceeds the log-normal method and a procedure using consol bonds. The efficiency gains greatly facilitate any estimation which is illustrated by considering a long-run risk model for the US. Allowing for an unconstrained intertemporal elasticity of substitution enhances the model’s fit, and we see further improvements when incorporating stochastic volatility and external habits.

Suggested Citation

  • Andreasen Martin M. & Zabczyk Pawel, 2015. "Efficient bond price approximations in non-linear equilibrium-based term structure models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(1), pages 1-33, February.
    • Handle: RePEc:bpj:sndecm:v:19:y:2015:i:1:p:1-33:n:1
    DOI: 10.1515/snde-2012-0005
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    References listed on IDEAS

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    1. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    2. De Paoli, Bianca & Scott, Alasdair & Weeken, Olaf, 2010. "Asset pricing implications of a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2056-2073, October.
    3. Rudebusch, Glenn D. & Swanson, Eric T., 2008. "Examining the bond premium puzzle with a DSGE model," Journal of Monetary Economics, Elsevier, vol. 55(Supplemen), pages 111-126, October.
    4. Ian W. R. Martin, 2008. "Disasters and the Welfare Cost of Uncertainty," American Economic Review, American Economic Association, vol. 98(2), pages 74-78, May.
    5. Eric T. Swanson, 2012. "Risk Aversion and the Labor Margin in Dynamic Equilibrium Models," American Economic Review, American Economic Association, vol. 102(4), pages 1663-1691, June.
    6. Andreasen, Martin M., 2012. "An estimated DSGE model: Explaining variation in nominal term premia, real term premia, and inflation risk premia," European Economic Review, Elsevier, vol. 56(8), pages 1656-1674.
    7. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    8. Juillard, Michel & Villemot, Sébastien, 2011. "Multi-country real business cycle models: Accuracy tests and test bench," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 178-185, February.
    9. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    10. Glenn D. Rudebusch & Eric T. Swanson, 2012. "The Bond Premium in a DSGE Model with Long-Run Real and Nominal Risks," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 105-143, January.
    11. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    12. van Binsbergen, Jules H. & Fernández-Villaverde, Jesús & Koijen, Ralph S.J. & Rubio-Ramírez, Juan, 2012. "The term structure of interest rates in a DSGE model with recursive preferences," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 634-648.
    13. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
    14. Tsionas, Efthymios G., 2003. "Exact solution of asset pricing models with arbitrary shock distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 843-851, March.
    15. Anh Le & Kenneth J. Singleton & Qiang Dai, 2010. "Discrete-Time Affine-super-ℚ Term Structure Models with Generalized Market Prices of Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2184-2227.
    16. Wu, Tao, 2006. "Macro Factors and the Affine Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(7), pages 1847-1875, October.
    17. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    18. Annette Vissing-Jorgensen, 2002. "Limited Asset Market Participation and the Elasticity of Intertemporal Substitution," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 825-853, August.
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    Cited by:

    1. Parra-Alvarez, Juan Carlos & Polattimur, Hamza & Posch, Olaf, 2021. "Risk matters: Breaking certainty equivalence in linear approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    2. Lorenzo Bretscher & Alex Hsu & Andrea Tamoni, 2017. "Level and Volatility Shocks to Fiscal Policy: Term Structure Implications," 2017 Meeting Papers 258, Society for Economic Dynamics.
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    4. Martin M. Andreasen & Anders Kronborg, 2017. "The Extended Perturbation Method: New Insights on the New Keynesian Model," CREATES Research Papers 2017-14, Department of Economics and Business Economics, Aarhus University.
    5. Martin Kliem & Alexander Meyer‐Gohde, 2022. "(Un)expected monetary policy shocks and term premia," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 477-499, April.

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    Keywords

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    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E0 - Macroeconomics and Monetary Economics - - General

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