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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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    More about this item

    Keywords

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

    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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