  Several studies have focused on the Realized Range Volatility, an estimator
of the quadratic variation of financial prices, taking into account the impact
of microstructure noise and jumps. However, none has considered direct modeling
and forecasting of the Realized Range conditional quantiles. This study carries
out a quantile regression analysis to fill this gap. The proposed model takes
into account as quantile predictors both the lagged values of the estimated
volatility and some key macroeconomic and financial variables, which provide
important information about the overall market trend and risk. In this way, and
without distributional assumptions on the realized range innovations, it is
possible to assess the entire conditional distribution of the estimated
volatility. This issue is a critical one for financial decision-makers in terms
of pricing, asset allocation, and risk management. The quantile regression
approach allows how the links among the involved variables change across the
quantiles levels to be analyzed. In addition, a rolling analysis is performed
in order to determine how the relationships that characterize the proposed
model evolve over time. The analysis is applied to sixteen stocks issued by
companies that operate in differing economic sectors of the U.S. market, and
the forecast accuracy is validated by means of suitable tests. The results show
evidence of the selected variables' relevant impacts and, particularly during
periods of market stress, highlights heterogeneous effects across quantiles.

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