Examining Volatility in the Equity and Oil Markets Through Volatility Swaps and the Volatility Skew

Abstract

This paper uses the risk-neutral implied volatility measure to study the behavior of implied volatility in the equity and oil markets. Risk-neutral implied volatility is more informationally effcient than the traditional Black-Scholes ATM implied volatility as it backs out implied volatility from a chain of options, allowing it to capture the information contained in the level and curvature of the volatility skew. The Volatility Index (VIX) and the Oil Volatility Index (OVX), measures of annualized 30 day risk- neutral implied volatility, are used to study the dynamics of implied volatility in the equity and oil markets. Additionally, these measures are used along with realized volatility to construct 30 day volatility swaps, whose payoffs are used to estimate the risk premium priced into each market. This study finds that the VIX moves inversely and asymmetrically to changes in the S&P 500 and at low levels predicts strong returns to the market index. A significant premium is charged to own volatility, however payoffs to volatility swaps spike with market uncertainty, suggesting that equity volatility swaps act as insurance policies. Interestingly, the OVX also rises with negative oil returns however its movement shows no relationship to positive oil returns. Additionally, an even higher volatility risk premium is charged to own volatility in the oil market, yet this paper does not find evidence that payoffs to oil volatility swaps are substantial in times of crisis. This questions whether oil volatility swaps can effectively hedge spikes in realized volatility as well as whether the risk premium is abnormally high. The paper finishes by examining the volatility skew and identifies information that the OVX can and cannot capture. The volatility skew is regressed onto oil's annualized 30 day volatility risk premium and an equation is presented to model the risk premium based on the level and curvature of the volatility skew.