Quantile Regression Analysis of Asymmetric Return-Volatility Relation

This paper uses quantile regression to investigate the asymmetric return-volatility phenomenon with the newly adapted and robust implied volatility indices VIX, VXN, VDAX and VSTOXX. A particular goal is to quantify the effects of positive and negative stock index returns at various quantiles of the implied volatility distribution. As the level of the new volatility index increases during market declines, we believe that the negative asymmetric return-volatility relationship should be significantly more pronounced at upper quantiles of the IV distribution than is indicated by ordinary least squares (OLS) regression. We find pronounced negative and asymmetric return-volatility relationships between each volatility index and its corresponding stock market index. The asymmetry increases monotonically when moving from the median quantile to the uppermost quantile (i.e., 95%); OLS thereby underestimates this relation at upper quantiles. Additionally, the asymmetry is pronounced with a volatility skew-adjusted new volatility index measure in comparison to the old at-themoney volatility index measure. The VIX volatility index presents the highest asymmetric return-volatility relationship, followed by the VSTOXX, VDAX and VXN volatility indices. Our findings have implications for trading strategies, hedging portfolios, pricing and hedging volatility derivatives, and risk management.