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Temporal Aggregation of Volatility Models

Author

Listed:
  • Nour Meddahi
  • Eric Renault
Abstract
In this paper, we consider temporal aggregation of volatility models. We introduce a semiparametric class of volatility models termed square-root stochastic autoregressive volatility (SR-SARV) and characterized by an autoregressive dynamic of the stochastic variance. Our class encompasses the usual GARCH models and various asymmetric GARCH models. Moreover, our stochastic volatility models are characterized by observable multiperiod conditional moment restrictions. The SR-SARV class is a natural extension of the weak GARCH models. Our extension has four advantages: i) we do not assume that the fourth moment is finite; ii) we allow for asymmetries (skewness, leverage effect) that are excluded by the weak GARCH models; iii) we derive conditional moment restrictions which are useful for non-linear inference; iv) our framework allows us to study temporal aggregation of IGARCH models and non-linear models such as EGARCH and Exponential SV in discrete and continuous time. Dans cet article, nous considérons l'agrégation temporelle des modèles de volatilité. Nous introduisons une classe de modèles de volatilité semi-paramétrique dénommée SR-SARV et caractérisée par une variance stochastique ayant une dynamique autorégressive. Notre classe contient les modèles GARCH usuels ainsi que plusieurs variantes asymétriques. De plus, nos modèles à volatilité stochastique sont caractérisés par des moments conditionnels observables et à plusieurs horizons. La classe des modèles SR-SARV est une généralisation naturelle des modèles GARCH faibles. Notre extension présente quatre avantages: i) nous ne supposons pas que le moment d'ordre quatre est fini; ii) nous permettons des asymétries (de type skewness et effet de levier) qui sont exclues par les modèles GARCH faibles; iii) nous dérivons des restrictions sur des moments conditionnels utiles pour l'inférence non-linéaire; iv) notre cadre de travail nous permet d'étudier l'agrégation temporelle des modèles IGARCH ainsi que des modèles non linéaires comme le modèle EGARCH et les modèles exponentiels à volatilité stochastique en temps discret et continu.

Suggested Citation

  • Nour Meddahi & Eric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO.
    • Handle: RePEc:cir:cirwor:2000s-22
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    References listed on IDEAS

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