You run an equities and equity-options trading group. A young quant analyst you have recently hired to fetch you sandwiches and coffee approaches you with a breathless tale of a red-hot profit opportunity from a market pricing inefficiency.

The analyst has identified a company, BellCurve Inc., whose historical equity returns over the last 6 years fit a normal distribution with constant volatility almost exactly. Yet, the analyst has documented that options on BellCurve's equity have historically had a pronounced implied volatility skew over this period. Specifically, out-of-the-money put options (those with low strike prices relative to the current price) have had higher implied volatilities than at-the-money options. Worse yet, the analyst notes, the skew has steepened in recent months.

The analyst argues that the volatility skew is inconsistent with the normality of returns, and therefore that the market has been systematically over-pricing out-of-the-money put options relative to those at-the-money. The steepening volatility skew is a sign that the mispricing is getting worse, so he suggests selling these overpriced options.

Assuming that the only reason for the existence of a volatility skew is anticipated fat tails in returns, is the analyst correct that there is a historical mispricing of options? Or is it possible that historical returns could be almost exactly normal, yet rationally-priced options could still exhibit a volatility skew?