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

Gianluca Benigno, Pierpaolo Benigno, Salvatore Nistic̣, December 2010
Paper No' CEPDP1033: | Full paper (pdf)
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Keywords: stochastic volatility; second order approximation

JEL Classification: C63

Is hard copy/paper copy available? YES - Paper Copy Still In Print.
This Paper is published under the following series: CEP Discussion Papers
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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.