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Higher-Order Effects in Asset-Pricing Models with Long-Run Risks


  • Ole Wilms

    (University of Zurich)

  • Karl Schmedders

    (University of Zurich)

  • Walt Pohl

    (University of Zurich)


This paper analyzes both the existence of solutions to long-run risk asset pricing models as well as the practicality of approximating these solutions by the Campbell-Shiller log-linearization. We prove a simple relative existence result that is sufficient to show that the original Bansal-Yaron model has a solution. Log-linearization fares less well: we find that for very persistent processes the approximation errors in model moments can be as large as 50%, and can get such basic facts wrong as the direction of the yield curve. The increasing complexity of state-of-the-art asset-pricing models can lead to complex nonlinear solutions with considerable curvature, which in turn can have sizable economic implications. Therefore, these models require numerical solution methods, such as the projection methods employed in this paper, that can adequately describe the higher-order equilibrium features.

Suggested Citation

  • Ole Wilms & Karl Schmedders & Walt Pohl, 2016. "Higher-Order Effects in Asset-Pricing Models with Long-Run Risks," 2016 Meeting Papers 306, Society for Economic Dynamics.
  • Handle: RePEc:red:sed016:306

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    References listed on IDEAS

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    Cited by:

    1. A. Ronald Gallant & Mohammad Jahan-Parvar & Hening Liu, 2018. "Does Smooth Ambiguity Matter for Asset Pricing?," International Finance Discussion Papers 1221, Board of Governors of the Federal Reserve System (U.S.).
    2. Alexis Akira Toda, 2018. "Data-based Automatic Discretization of Nonparametric Distributions," Papers 1805.00896,, revised May 2019.
    3. Ivan Sutoris, 2018. "Asset Prices in a Production Economy with Long Run and Idiosyncratic Risk," CERGE-EI Working Papers wp620, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    4. Oliver de Groot & Alexander W. Richter & Nathaniel A. Throckmorton, 2018. "Valuation Risk Revalued," CDMA Working Paper Series 201803, Centre for Dynamic Macroeconomic Analysis.
    5. Andreas Tryphonides, 2018. "Equilibrium Restrictions and Approximate Models: Pricing Macroeconomic Risk," Papers 1805.10869,
    6. Myroslav Pidkuyko & Raffaele Rossi & Klaus Reiner Schenk-Hoppé, 2019. "The Resolution of Long-Run Risk," The School of Economics Discussion Paper Series 1908, Economics, The University of Manchester.

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