  This paper investigates how the conditional quantiles of future returns and
volatility of financial assets vary with various measures of ex-post variation
in asset prices as well as option-implied volatility. We work in the flexible
quantile regression framework and rely on recently developed model-free
measures of integrated variance, upside and downside semivariance, and jump
variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show
that simple linear quantile regressions for returns and heterogenous quantile
autoregressions for realized volatility perform very well in capturing the
dynamics of the respective conditional distributions, both in absolute terms as
well as relative to a couple of well-established benchmark models. The models
can therefore serve as useful risk management tools for investors trading the
futures contracts themselves or various derivative contracts written on
realized volatility.
