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Analytic Evaluation of Volatility Forecasts

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  • Torben G. Andersen
  • Tim Bollerslev
  • Nour Meddahi

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Abstract

The development of estimation and forecasting procedures using empirically realistic continuous-time stochastic volatility models is severely hampered by the lack of closed-form expressions for the transition densities of the observed returns. In response to this, Andersen, Bollerslev, Diebold and Labys (2002) have recently advocated modeling and forecasting the (latent) integrated volatility of primary import from a pricing perspective based on simple reduced form time series models for the observable realized volatilities, constructed from the summation of high-frequency squared returns. Building on the eigenfunction stochastic volatility class of models introduced by Meddahi (2001), we present analytical expressions for the loss in forecast efficiency associated with this easy-to-implement procedure as a function of the sampling frequency of the returns underlying the realized volatility measures. On numerically quantifying this efficiency loss for such popular continuous-time models as GARCH, multi-factor affine, and log-normal diffusions, we find that the realized volatility reduced form procedures perform remarkably well in comparison to the optimal (non-feasible) forecasts conditional on the full sample path realization of the latent instantaneous volatility process. Le développement de procédures d'estimation et de prévision utilisant des modèles réalistes, en temps continu et à volatilité stochastique est sévèrement bloqué par la non disponibilité de la densité de transition des rendements. En réponse à ce problème, Andersen, Bollerslev, Diebold et Labys (2002) ont récemment proposé de modéliser et de prévoir la volatilité intégrée (et inobservable), qui est importante pour la valorisation des produits dérivés, à partir de formes réduites simples de la volatilité réalisée, calculée en sommant des carrés des rendements à haute fréquence. En utilisant la classe de modèles à volatilité stochastique basée sur des fonctions propres introduites dans Meddahi (2001), nous présentons les expressions analytiques des fonctions de pertes de ces prévisions simples en fonction du pas de temps des rendements à haute fréquence. En quantifiant ces fonctions de pertes pour les modèles en temps continu usuels comme les modèles de diffusion GARCH, affine à plusieurs facteurs, et log-normal, nous trouvons que les procédures à base de formes réduites se comportent très bien par rapport aux procédures optimales (et infaisables) qui utilisent toute la trajectoire de la volatilité instantanée et inobservable.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-90.

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Date of creation: 01 Dec 2002
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Handle: RePEc:cir:cirwor:2002s-90

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Keywords: Continuous-time models; eigenfunction stochastic volatility models; integrated volatility; realized volatility; high-frequency data; time series forecasting; Mincer-Zarnowitz regressions; modèles à temps continu; modèles à volatilité stochastique basée sur des fonctions propres; volatilité intégrée; volatilité réalisée; données à haute fréquence; prévision de séries chronologiques; régressions de Mincer-Zarnowitz;

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References

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