Second-Order Approximation of Dynamic Models with Time-Varying Risk
25 Pages Posted: 27 Dec 2010 Last revised: 14 Jun 2023
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Second-Order Approximation of Dynamic Models with Time-Varying Risk
Second Order Approximation of Dynamic Models with Time-Varying Risk
Date Written: December 2010
Abstract
This paper provides first and second-order approximation methods for the solution of non-linear dynamic stochastic models in which the exogenous state variables follow conditionally-linear stochastic processes displaying time-varying risk. The first-order approximation is consistent with a conditionally-linear model in which risk is still time-varying but has no distinct role -- separated from the primitive stochastic disturbances -- in influencing the endogenous variables. The second-order approximation of the solution, instead, is sufficient to get this role. Moreover, risk premia, evaluated using only a first-order approximation of the solution, will be also time varying.
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