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What order? Perturbation methods for stochastic volatility asset pricing and business cycle models

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  • Oliver de Groot

    () (School of Economics and Finance, University of St Andrews)

Abstract

When a DSGE model features stochastic volatility, is a third-order perturbation approximation sufficient? The answer is often no. A key parameter - the standard deviation of stochastic volatility innovations - does not appear in the coefficients of the decision rules of endogenous variables until a fourth- or sixth-order perturbation approximation (depending on the functional form of the stochastic volatility process). This paper shows analytically this general result and demonstrates, using three models, that important model moments can be imprecisely measured when the order of approximation is too low. i) In the Bansal-Yaron long-run risk model, the equity risk premium rises from 4.5% to 10% by going to sixth-order. ii) In a workhorse real business cycle model, the welfare cost of business cycles also rise when a fourth-order approximation properly accounts for the presence of stochastic volatility. iii) In a canonical New-Keynesian model, the risk-aversion parameter can be lowered while matching the term premium when a fourth-order approximation is used.

Suggested Citation

  • Oliver de Groot, 2016. "What order? Perturbation methods for stochastic volatility asset pricing and business cycle models," CDMA Working Paper Series 201606, Centre for Dynamic Macroeconomic Analysis.
  • Handle: RePEc:san:cdmawp:1606
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    Keywords

    Numerical solution methods; Time-varying uncertainty; Equity premium; DSGE models; Welfare;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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