Second-Order Approximation of Dynamic Models with Time-Varying Risk
Paper No' CEPDP1033:
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Keywords: stochastic volatility; second order approximation
JEL Classification: C63
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This Paper is published under the following series:
CEP Discussion Papers
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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.