Undervalued Options

Options are empirically undervalued, especially the fat tails, which means the seller actually has a negative expectancy. Over a small series of data points, the expectancy is relatively flat. However, over a large series of data points, options become more and more undervalued. How is this possible? Because it's not possible to price a put on 9/11. It's not possible to price a put on Enron. It's not possible to price a put for the crash of 87. These puts are substantially undervalued. What this means is, if you sell enough puts over a long enough period of time, your expectancy will go from zero to more and more negative. There have been numerous amounts of academic papers written in the difficulties of pricing fat tail options. It's not that rare events happen more frequently then we think (they do) it's that rare events are seriously underpriced. Again, there are no "positive edge" options.