Second-Order Approximation of Dynamic Models with Time-Varying Risk

Abstract

This paper provides first and second-order approximation methods for the solution of nonlinear 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 timevarying 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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Cite this paper

@inproceedings{Benigno2010SecondOrderAO, title={Second-Order Approximation of Dynamic Models with Time-Varying Risk}, author={Gianluca Benigno and Pierpaolo Benigno and Salvatore Nistic{\'o}}, year={2010} }