With the increasing availability of high frequency financial data, the development of realized variance (RV) has made tremendous progress both on the theoretical front and in empirical applications, (see for instance Andersen and Bollerslev, 1998; Andersen, Bollerslev, Diebold, and Labys, 2001, 2003; Barndorff Nielsen and Shephard, 2004a). The focus of this literature is the construction of a flexible model-free measure of integrated variance for asset returns.
It is shown that RV is a consistent estimator of the integrated variance provided that the asset price process is a continuous semi-martingale. There are many advantages associated with the model-free RV measure. For example, when the objective is to evaluate the predictive power of certain models, such as ARCH/GARCH, the RV can be used as a proxy for the unobserved conditional variance. In addition, the computation of RV is straightforward, simply the sum of squared intra period returns.
While the non-parametric nature of RV can be a considerable advantage, practical applications often call for a variance measure that is consistent with a structural model. In financial applications, dynamic asset return models are indispensable tools for, for instance, pricing and hedging derivatives, asset allocation, risk management, etc. Since variance is often a crucial input variable, it is thus important for the variance estimator to be consistent with the model structure.
Moreover, from a statistical viewpoint, specification of a model can lead to more efficient use of information by exploiting dynamic relationships that are inherent in the data generating processes. For instance, a model-based variance measure can lead to enhanced precision by explicitly incorporating the well-documented empirical evidence that asset return variance is temporally persistent. While the RV concept builds on Merton’s (1980) insight that high frequency returns can improve the efficiency of variance estimates, the persistence of stochastic volatility can be exploited to further improve efficiency through smoothing over extended horizons.
In this paper, we develop new model-based variance measures that explicitly incorporate the smoothing idea. In particular, unbiased estimators of both spot variance and integrated variance are derived in the continuous time affine jump-diffusion framework of Duffie, Pan, and Singleton (2000). We focus on this class of models as they are commonly used in the finance literature for the modeling of asset returns, but note that this approach can be extended to a more general class of dynamic latent variable processes. The derivation of the variance estimators exploits the dynamic relationship between the latent variance and the observed asset returns.
Unbiased estimators of spot and integrated variance are then constructed using return observations over extended forward and backward horizons. Intuitively, the spot variance estimator can be viewed as the weighted sum of squared returns where the weights are explicitly determined by the model structure and can be set as optimal to ensure minimum variance of the estimators. Similarly, the integrated variance estimator can be viewed as the weighted sum of realized variances.
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Model-based variance measures and the market information content
