Quantile Models Linking Returns and Volatility to Price Variation

Summary

This paper examines how measures of past price variation and option-implied volatility relate to the conditional distributions of future returns and realized volatility. It focuses on integrated variance, upside and downside semivariance, and jump variation, using flexible quantile regression to model outcomes across different parts of their distributions.

For S&P 500 and WTI crude oil futures, the study finds that linear quantile regressions for returns and heterogeneous quantile autoregressions for realized volatility capture distribution dynamics effectively. It compares these approaches with established benchmark models and reports strong performance both in absolute terms and relative to those benchmarks. The results suggest potential use in assessing risk for futures and contracts tied to realized volatility. The evidence is specific to the two futures markets studied; the document does not provide further detail on implementation choices or performance in other assets or periods.

Key ideas

• Quantile regression can describe how predictors relate to different parts of future return distributions.
• Integrated variance, semivariances, jump variation, and implied volatility are considered as predictors.
• Linear quantile models are used for returns, while heterogeneous quantile autoregressions model realized volatility.
• The reported evidence covers S&P 500 and WTI crude oil futures and includes comparisons with benchmark models.
• The models may support risk assessment for futures and realized volatility derivatives.

Tags

# Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility


# Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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