Practical Applications of Value for Equity Index Options: Expected—Not Realized—Volatility and the Distribution of Forecasts

Abstract

In Value for Equity Index Options: Expected—Not Realized—Volatility and the Distribution of Forecasts, from the November 2022 issue of The Journal of Portfolio Management, J. Benson Durham of Piper Sandler demonstrates that anticipated rather than “realized” volatility is more useful for option traders and other investors who must assess the levels of risk and fear in option markets. Durham estimates expected volatility and the distribution around volatility forecasts using six generalized autoregressive conditional heteroskedasticity (GARCH) models. GARCH is a statistical approach that analyzes time-series data to estimate the amount of volatility and the changes in volatility over time, as opposed to common measures based on arbitrarily chosen rolling windows or asset returns. Durham argues that using multiple GARCH models gives practitioners a better, forward-looking estimate of implied volatility, the key input in option pricing models. Durham offers investment practitioners an alternative method for determining the value of at-the-money equity options. His approach departs from the traditional, backward-looking volatility inputs commonly used in option models. Further, he explains that implied volatility embeds not only expected volatility, but also a risk premium for variation in volatility. He underscores the importance of incorporating forward-looking instead of historical inputs for equity option valuation because all asset prices reflect expectations for the future, not the past.