Nonparametric Leverage and Volatility Feedback Effects and Nonparametric Conditional Dependence Between S&P 500 Index Returns and Log-Increments of Implied Volatility Index (VIX)∗

This paper studies contemporaneous relationship between S&P 500 index returns and logincrements of the market volatility index (VIX) via a nonparametric copula method. Specifically, we propose a conditional dependence index to investigate how the dependence between the two series varies across different segments of the market return distribution. We observe the following findings: (a) the two series exhibit strong, negative, extreme tail dependence; (b) the negative dependence is stronger in extreme bearish markets than in extreme bullish markets; (c) the dependence gradually weakens as the market return moves toward the center of its distribution, or in quiet markets. The unique dependence structure supports the VIX as a barometer of markets’mood in general. Applying the proposed method to the S&P 500 returns and the implied variance (VIX), we find that the nonparametric leverage effect is much stronger than the nonparametric volatility feedback effect, although, in general, both effects are weaker than the dependence relation between the market returns and the log-increments of the VIX.