Leverage and Volatility Feedback Effects in High-Frequency Data

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Abstract
We examine the relationship between volatility and past and future returns in high-frequency equity market data. Consistent with a prolonged leverage effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be significantly negative for several days, while the reverse cross-correlations between absolute returns and future returns are generally negligible. Based on a simple aggregation formula, we demonstrate how the high-frequency data may similarly be used in more effectively assessing volatility asymmetries over longer daily return horizons. Motivated by the striking cross-correlation patterns uncovered in the high-frequency data, we investigate the ability of some popular continuous-time stochastic volatility models for explaining the observed asymmetries. Our results clearly highlight the importance of allowing for multiple latent volatility factors at very fine time scales in order to adequately describe and understand the patterns in the data.