HAR volatility modelling with heterogeneous ... - ResearchGate

1 IntroductionThe importance of financial market volatility led to a very large literature in which volatilitydynamics has been modelled to take into accunt its most salient features (clustering,slowly decaying auto-correlation, asymmetric responses). This paper contributes to thisliterature by proposing a reduced form discrete-time model in which, after separatingquadratic variation in the continuous and jumps part, 1 volatility is assumed to depend onthree components: continuous volatility, negative returns and jumps. In order to reproducethe persistent impact of each component observed in the data, we impose a commonheterogeneous structure. In particular, while it is well known that volatility tends toincrease more after a negative shock than after a positive shock of the same magnitude,see Christie (1982); Campbell and Hentschel (1992); Glosten et al. (1989) and more recentlyBollerslev et al. (2006), we provide novel evidence on the fact that the impact ofnegative returns on future volatility (the so-called leverage effect) is also highly persistentand extends for a period of at least one month.In Corsi (2009) a simple Heterogeneous Auto-Regressive (HAR) model has been proposedfor realized volatility to capture the empirical memory persistence of volatility in a simpleand parsimonious way. In this paper, we propose an extended version of the HAR modelwhich considers asymmetric responses of the realized volatility not only to previous dailynegative returns, but also to their weekly and monthly aggregation. Our main contributionis then to show that the heterogeneous structure applies to the leverage effect as well, thusreinforcing the Heterogeneous Market Hypothesis of Muller et al. (1997).In addition, we study the impact on future volatility of jumps (discontinuous variationsof the asset price) measured over the same three different horizons. Given the inadequacyof bipower variation in measuring volatility in presence of jumps, we use the tests and1 Several techniques for separating the continuous variation from the discontinuous variation have beenexplored in Barndorff-Nielsen and Shephard (2004); Mancini (2009); Corsi et al. (2009); Andersen et al.(2008) among others.2