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

Abstract

• Our empirical analysis makes use of high-frequency data from the futures markets. • We show that the introduction of both leverage and jumps in the futures return dynamics improves the ability to forecast volatility. • It also provides the best forecast for risk in both a VaR and a CVaR sense. • It benefits speculative firms who are short natural gas futures while minimizing tail risk in a VaR sense. • And it also benefits speculative firms who are long S&P500 futures and use either VaR or CVaR as financial risk management criteria. In this paper, we propose a model for futures returns that has the potential to provide both individual investors and firms who have positions in financial and energy commodity futures a valid tail risk management tool. In doing so, we also aim to explore the commonalities between these markets and the degree of financialization of energy commodities. While empirical studies in energy markets embed either leverage or jumps in the futures return dynamics, we show that the introduction of both features improves the ability to forecast volatility as an indicator for risk for both the S&P500 and natural gas futures markets.