Volatility asymmetry in high-frequency data

My dissertation examines the important stylized fact of asymmetric volatility in high frequency data. Empirical study of the lead-lag relation between volatility and returns in high frequency data reveals a new prolonged and slowly decreasing impact of the current returns on the future volatility that is significant for around three days. Also derived is a temporal aggregation formula for the correlation between squared returns and lagged returns that permits more accurate measures of the daily correlation using high frequency data.; The dissertation then examines the ability of specific stochastic volatility models to fit the daily and hourly data and to explain the pattern observed in high and low frequency data. Most of the simple models widely used in practice today fail to produce this pattern. I consider a logarithmic two-factor stochastic volatility model and estimate it using the efficient method of moments (EMM). The presence of two volatility factors breaks the link between tail thickness and volatility persistence. The two-factor model provides a good fit to the daily data but generates a cross-correlation pattern that is different from that observed in the high frequency data. The same model is rejected when estimated using the hourly data but generates a pattern close to that observed in the high and low frequency data.; Lastly, my dissertation discusses the time varying leverage hypothesis and possible ways to model it. While there is no evidence of a time varying leverage effect in the daily data, the hourly data supports the hypothesis of a time varying correlation.