Risk Matters: Breaking Certainty Equivalence in Linear Approximations

58 Pages Posted: 18 May 2018 Last revised: 29 Oct 2020

See all articles by Juan Carlos Parra-Alvarez

Juan Carlos Parra-Alvarez

Aarhus University - CREATES

Hamza Polattimur

University of Hamburg

Olaf Posch

Universität Hamburg, Department of Economics; CREATES

Date Written: September 2020

Abstract

In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We study the extent to which a first-order approximated solution built by perturbation methods accounts for risk. We show that risk matters economically in a real business cycle (RBC) model with habit formation, and capital adjustment costs and that neglecting risk leads to substantial pricing errors. A first-order approximation in continuous time reduces pricing errors by 90 percent relative to the certainty equivalent linear solution.

Keywords: Certainty equivalence, Perturbation methods, Pricing errors

JEL Classification: C02, C61, C63, E13, E32, G12

Suggested Citation

Parra-Alvarez, Juan Carlos and Polattimur, Hamza and Posch, Olaf, Risk Matters: Breaking Certainty Equivalence in Linear Approximations (September 2020). Available at SSRN: https://ssrn.com/abstract=3173519 or http://dx.doi.org/10.2139/ssrn.3173519

Juan Carlos Parra-Alvarez (Contact Author)

Aarhus University - CREATES ( email )

Department of Economics and Business
Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Hamza Polattimur

University of Hamburg ( email )

Allende-Platz 1
Hamburg, 20146
Germany

Olaf Posch

Universität Hamburg, Department of Economics ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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