Multivariate volatility forecasts for stock market indices

Volatility forecasts aim to measure future risk and they are key inputs for financial analysis. In this study, we forecast the realized variance as an observable of volatility several major international stock market indices accounted different predictive information present in jump, continuous, option-implied components. We allowed spillovers markets by using a multivariate modeling approach. used heterogeneous autoregressive (HAR)-type models obtain forecasts. Based out-of-sample show that: (i) including variances HAR model substantially improves accuracy, (ii) lasso-based lag selection methods do not outperform parsimonious day-week-month structure model, (iii) cross-market spillover effects embedded have long-term forecasting power.