HAR volatility modelling with heterogeneous ... - ResearchGate

et al. (2008) implement it for risk management with VaR measures; Bollerslev et al. (2008)use it to analyze the risk-return tradeoff; Bianco et al. (2009) use it to study the relationbetween intraday serial correlation and volatility.It is then natural to extend the Heterogeneous Market Hypothesis approach to leverageeffect. We assume that asymmetric responses of realized volatility not only to previousdaily returns but also to past weekly and monthly returns. We model such heterogeneousleverage effects by introducing asymmetric return-volatility dependence at each level ofthe cascade considered in the above section. Define daily returns r t = X t −X t−1 and pastaggregated negative returns as:r (n)−t = 1 n (r t + ... + r t−n+1 )I {(rt+...+r t−n+1 )