Risk-Adjusted Linearizations of Dynamic Equilibrium Models

42 Pages Posted: 11 Dec 2018

See all articles by Pierlauro Lopez

Pierlauro Lopez

Banque de France

J. David López-Salido

Board of Governors of the Federal Reserve System

Francisco Vazquez-Grande

Board of Governors of the Federal Reserve System

Multiple version iconThere are 2 versions of this paper

Date Written: December 2018

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

JEL Classification: C63, G12, E32, E44

Suggested Citation

Lopez, Pierlauro and López-Salido, J. David and Vazquez-Grande, Francisco, Risk-Adjusted Linearizations of Dynamic Equilibrium Models (December 2018). Banque de France Working Paper No. 702. Available at SSRN: https://ssrn.com/abstract=3297568 or http://dx.doi.org/10.2139/ssrn.3297568

Pierlauro Lopez (Contact Author)

Banque de France ( email )

Paris
France

J. David López-Salido

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Francisco Vazquez-Grande

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States
202-973-7488 (Phone)

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