Predictive Inference for Integrated Volatility

In recent years, numerous volatility-based derivative products have been engineered. This has led to interest in constructing conditional predictive densities and confidence intervals for integrated volatility. In this paper, we propose nonparametric kernel estimators of the aforementioned quantities. The kernel functions used in our analysis are based on different realized volatility measures, which are constructed using the ex post variation of asset prices. A set of sufficient conditions under which the estimators are asymptotically equivalent to their unfeasible counterparts, based on the unobservable volatility process, is provided. Asymptotic normality is also established. The efficacy of the estimators is examined via Monte Carlo experimentation, and an empirical illustration based upon data from the New York Stock Exchange is provided.