Stochastic volatility, jumps and leverage in energy and stock markets

Abstract

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. Unlike most of the existing studies in energy derivative markets based on daily data, our empirical analysis makes use of high-frequency (tick-by-tick) data from the futures markets, aggregated to 10-minute intervals during the trading day. The intraday variation is then utilized to generate daily time series of prices, returns and realized variance. We estimate stochastic volatility models using a GMM approach based on the moment conditions of the Integrated Volatility derived from high frequency data. While existing 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 using both the RMSE and MAE criteria. Our analysis also shows that overall, the introduction of both leverage and jumps in the SVJL model provides the best forecast for risk in both a VaR and a CVaR sense for investors who have any position in natural gas futures regardless of their degree of risk aversion. In the S&P500 market, the SVJL model provides the most precise forecast of risk in a CVaR sense for risk-averse investors with any position in futures, regardless of their degree of risk aversion. Focusing on a firm's internal risk management, the introduction of both jumps and leverage in the SVJL model would benefit speculative firms who are short natural gas futures aiming at minimizing tail risk in a VaR sense, as well as speculative firms who are long S&P500 futures and use either VaR or CVaR as financial risk management criteria while wanting to minimize the opportunity cost of capital.