Stochastic volatility, jumps and leverage in energy and stock markets:evidence from high frequency data

The study of volatility in crude oil and natural gas markets and its interac- tion with returns (leverage) has a broad range of financial impacts both from a hedging point of view and also for forecasting purposes.The main limitation of using daily data is that volatility is not observable. In contrast, intra-day data provide an almost continuous observation of the return series, making volatility observable. From an econometric point of view, the employment of intra-day data leads to the estimation of structural parameters of stochastic volatility models using simple moment conditions while fitting all the relevant empirical features of energy and stock index returns. This paper contributes to the current debate by: 1) exploring evidence of leverage effects and jumps in energy futures markets versus financial stock indexes (S&P500) and 2) evalu- ating the impact of leverage on risk forecasting in a VaR and CVaR sense. We find significant evidence of a leverage effect for S&P500 and crude oil markets: a negative shock to returns increases volatility in these markets. We also find evidence of an inverse leverage effect for the natural gas market: volatility becomes higher when energy returns increase. We also find evidence for jumps in the energy futures markets. We show that the introduction of leverage improves the forecasting ability of the SV model using the RMSE and MAE criteria for all the markets considered while introducing jumps improves only the ability of modeling the behaviour of the volatility for the crude oil futures market.