Properties of High Frequency DAX Returns: Intraday Patterns, Jumps and their Impact on Subsequent Volatility

This paper analyzes the behavior of the German DAX index intraday returns. We devote particular attention to three related empirical issues. First we provide an up-to-date characterization of the DAX intraday volatility patterns. They are mostly W-shaped with peaks at the opening, at 2.30pm and before the closing. We find some evidence suggesting that the implied volatility also follows some deterministic patterns over the trading day. Second we identify jumps in DAX returns. On jump days, they account on average for 15% to 25% of the daily variance. Jumps also tend to cluster and are not evenly distributed throughout the trading day. Third we estimate the impact of a price jump on volatility. We consider different proxies for volatility: absolute returns, implied volatility and realized volatility. Our results indicate that negative jumps trigger a strong upward correction in volatility. This correction starts just after a jump occured and persists during up to 25 minutes. On the other hand, positive jumps seem to have a much less significant impact on volatility. These results hold for all volatility proxies but they are more significant when we consider the implied volatility.