A High‐Frequency Investigation of the Interaction between Volatility and DAX Returns

Abstract

One of the most noticeable stylised facts in finance is that stock index returns are negatively correlated with changes in volatility. The economic rationale for the effect is still controversial. The competing explanations have different implications for the origin of the relationship: Are volatility changes induced by index movements, or inversely, does volatility drive index returns? To differentiate between the alternative hypotheses, we analyse the lead-lag relationship of option implied volatility and index return in Germany based on Granger causality tests and impulse-response functions. Our dataset consists of all transactions in DAX options and futures over the time period from 1995 to 2005. Analyzing returns over 5-minute intervals, we find that the relationship is return-driven in the sense that index returns Granger cause volatility changes. This causal relationship is statistically and economically significant and can be clearly separated from the contemporaneous correlation. The largest part of the implied volatility response occurs immediately, but we also observe a smaller retarded reaction for up to one hour. A volatility feedback effect is not discernible. If it exists, the stock market appears to correctly anticipate its importance for index returns.

Low Risk and High Return – Affective Attitudes and Stock Market Expectations

“…The empirical literature on the variance-return relationship is mixed (for a discussion, see Poon and Taylor, 1992;Subrahmanyam, 2010). It has documented both, positive as well as negative correlations between variance and return of stocks (Masset and Wallmeier, 2010). We compute crosssectional correlations between realised returns, variance, systematic and unsystematic risk of all stocks used in our analysis during the year of and the year before the experiment (i.e.…”

Stochastic Volatility Jump‐Diffusions for European Equity Index Dynamics

“…Therefore, to keep the model as parsimonious as possible, we drop such any dependence on the variance from the drift specification. 4 New evidence regarding the origin of the leverage effect for the DAX is presented in Masset and Wallmeier (2010).…”

“…New evidence regarding the origin of the leverage effect for the DAX is presented in Masset and Wallmeier ().…”

Measuring High-Frequency Causality between Returns, Realized Volatility and Implied Volatility

“…5 This finding can be contrasted with the one of Masset and Wallmeier (2010), who also used highfrequency data to analyze the lead-lag relationship of option implied volatility and index return in Germany, using Granger causality tests (at horizon one) and impulse-response functions. They find that the relationship is return-driven in the sense that index returns Granger cause volatility changes.…”