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Risk-Adjusted Linearizations of Dynamic Equilibrium Models

Author

Listed:
  • Pierlauro Lopez
  • David Lopez-Salido
  • Francisco Vazquez-Grande

Abstract

We propose a simple risk-adjusted linear approximation to solve a large class of dynamic models with time-varying and non-Gaussian risk. Our approach generalizes lognormal affine approximations commonly used in the macro-finance literature and can be seen as a first-order perturbation around the risky steady state. Therefore, we unify coexisting theories of risk-adjusted linearizations. We provide a formal foundation for approximation methods that remained so far heuristic, and offer explicit formulas for approximate equilibrium objects and conditions for their local existence and uniqueness. Affine approximations are not nested in conventional perturbations of arbitrary order. We apply this technique to models featuring Campbell-Cochrane habits, recursive preferences, and time-varying disaster risk. The proposed affine approximation performs similarly to global solution methods in many applications; risk pricing is accurate at all investment horizons, thereby capturing the main properties of investors’ marginal utility of wealth and measures of welfare costs of fluctuations.

Suggested Citation

  • Pierlauro Lopez & David Lopez-Salido & Francisco Vazquez-Grande, 2018. "Risk-Adjusted Linearizations of Dynamic Equilibrium Models," Working papers 702, Banque de France.
  • Handle: RePEc:bfr:banfra:702
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    References listed on IDEAS

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    Cited by:

    1. Patrick Kehoe & Elena Pastorino & Pierlauro Lopez & Virgiliu Midrigan, 2018. "Asset Prices and Unemployment Fluctuations," 2018 Meeting Papers 1119, Society for Economic Dynamics.
    2. Juan Carlos Parra-Alvarez & Hamza Polattimur & Olaf Posch, 2020. "Risk Matters: Breaking Certainty Equivalence," CREATES Research Papers 2020-02, Department of Economics and Business Economics, Aarhus University.
    3. 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).
    4. Pierlauro Lopez, 2021. "Welfare Implications of Asset Pricing Facts: Should Central Banks Fill Gaps or Remove Volatility?," Working Papers 21-16R, Federal Reserve Bank of Cleveland, revised 16 May 2023.

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    More about this item

    Keywords

    Perturbation methods; Risky steady state; Macroeconomic uncertainty; Intertemporal risk prices; Risk-return tradeoff.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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