The basic idea behind "the black swan" is that given a limited sample it's foolish to try and estimate the probability of tail events, and thus in particular th

The basic idea behind "the black swan" is that given a limited sample it's foolish to try and estimate the probability of tail events, and thus in particular the expected value of convex functions. Say for instance you have a random variable which follows the following mixture: draw from a standard normal 99.99% of the time and from a standard normal 10 standards deviations away 0.01% of the time. If you collect 1,000 sample, 90% of the time you won't see a single instance where the value was drawn from the second mode. You plot your data and find that it perfectly fits a normal distribution. Neat! I then ask you, what the probability to get an event >10 standard deviation away. You punch in the numbers and come up with 1.31e-23. The real answer was about 1/20000. You're wrong by about 19 orders of magnitude. Moral of the story: if your model spits a probability much lower than the inverse of the sample size, don't trust it. Many financial instrument, like options, display convexity. This places greater emphasis on the tails of the distribution than on the center. If the option seller underestimates tail risk, it would be profitable on average to buy such options. There are many reasons why they might underestimate tail risk. They could ignore the theoretical argument I've exposed above. It could be that in a marketplace, sellers who ignore tail risk can stay in business long enough to put those who don't out of business.