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


  • Andreasen Martin M.


  • Zabczyk Pawel

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


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

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    1. 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.
    2. Martin M. Andreasen & Anders Kronborg, 2803. "The Extended Perturbation Method: New Insights on the New Keynesian Model," CREATES Research Papers 2017-14, Department of Economics and Business Economics, Aarhus University.
    3. Kliem, Martin & Meyer-Gohde, Alexander, 2017. "(Un)expected monetary policy shocks and term premia," Discussion Papers 30/2017, Deutsche Bundesbank.

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