Forecast Errors on the Implied Volatility of Equity Options

This thesis investigates the rational pricing of S&P 500 index options from 1996 to 2022. This is done by first using the Stein (1989) method to investigate the dynamics of the mean reversion of implied variances. Secondly, we will inspect the predictability of ex-post forecast errors of implied variance using ex-ante forecast revisions, and the impact of uncertainty on this relationship.

We find that long-term options tend to overreact to changes in the implied variances of short-term options. Furthermore, we find that forecast errors are predictable from forecast revisions, suggesting a degree of information rigidity among investors. This implies a systematic bias where upward revisions to forecasts predict higher future realizations, indicating that forecast adjustments are too conservative, and causes underreaction for short-term options.

By adding the uncertainty variable to the model, we can see that uncertainty significantly influences forecast revision and that a higher level of uncertainty results in a larger underestimation of forecasts. These findings are further tested through a trading strategy based on forecast revisions. The strategy produces high average monthly returns. However, the high volatility suggests that while the strategy is profitable, it comes with significant risk.

The research methodology employed a two-pronged approach. First, the Stein (1989) method was used to analyze the mean reversion dynamics of implied variances across options with different maturities. This allowed for a robust examination of how information flows between short-term and long-term option prices.

Second, a novel approach was developed to assess the predictability of forecast errors using forecast revisions, incorporating uncertainty as a key variable. This framework provided insights into how market participants process new information and adjust their expectations, particularly during periods of varying uncertainty.