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Risk-Adjusted Linearizations of Dynamic Equilibrium Models

Pierlauro Lopez, David Lopez-Salido and Francisco Vazquez-Grande

Working papers from Banque de France

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.

Keywords: Perturbation methods; Risky steady state; Macroeconomic uncertainty; Intertemporal risk prices; Risk-return tradeoff. (search for similar items in EconPapers)
JEL-codes: C63 G12 E32 E44 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-hea, nep-mac, nep-ore and nep-upt
Date: 2018
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