Why Rare-Event Option Profits Do Not Prove Mispricing
Summary
The discussion examines whether options on unlikely events are systematically underpriced, prompted by a story of a fund buying cheap-seeming tail-risk exposure. A large payoff from a rare event does not establish that the option was cheap: the event may have occurred even if the premium was fair or expensive. Assessing pricing requires repeated observations, which are hard to obtain for genuinely rare events, so apparent success can reflect luck.
The answer also cautions that rare-event options are not always cheap. Equity skew and crash protection may be expensive relative to historical experience, potentially reflecting demand for lottery-like payoffs or sound reasons to insure against severe losses. Any mathematical estimate depends on assumptions that may not match reality. The exchange gives conceptual arguments and references, rather than a controlled test or evidence that a particular strategy remains profitable after becoming public.
Key ideas
- A large gain from one rare event does not show that the option was underpriced.
- Repeated observations are needed to evaluate rare-event pricing, but such evidence is difficult to gather.
- Some forms of crash protection may be overpriced rather than underpriced.
- Behavioral demand for lottery-like payoffs and model assumptions can both affect option prices.
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Full text
# Why would the market systematically underestimate the probability of unlikely events? # Why would the market systematically underestimate the probability of unlikely events? (I'm not in finance, so pardon my ignorance) In The Big Short (2015), there is a little story about Cornwall Capital's early trading strategy: > Their strategy was simple and brilliant. Jamie and Charlie found markets will sell options very cheaply on things they think will never happen. So when they were wrong, they were wrong small, but when they were right, they were right big. There must have been a lot of such unlikely events that occurred, since their fund turned \$110K into \$30M in a few years. What I don't understand is why the market would systematically underestimate the probability of many unlikely events? Presumably, such estimates were based on some mathematical models, and not someone's gut instinct. Why would a bias such as this exist? Is it safe to assume that Cornwall Capital's strategy wouldn't work now, since it's been made public? ## Answer by Ivan (score 3, accepted) https://quant.stackexchange.com/a/54143 It’s a nice story and it makes for nice headlines and good reading (it’s a great book and movie) but it’s not necessarily that simple. You may or may not have the same view as your counterparty regarding the probability of some remote event and one of you may be “mispricing it” but the fact that it (or a few of them) happens and makes your fund $30m doesn’t imply the option was underpriced in the first place. It may have been, or it may actually have been expensive but the event occured nonetheless and you still made 100x your money even though at the fair price you would have made 200x. The only way to know is to repeat the same experiment many times. Obviously with rare events happening in the real world, it’s not that easy as it’s not a controlled experiment. It’s entirely possible that these types of funds are just lucky three times, ten times, in a row. There is not enough information to conclude that such or such option is mispriced. From experience though, certains classes of rare events like market crashes tend to be overpriced: equity skew is “too high” and “cliquet crash puts” are “too expensive” by most measures against history and there are good theoretical reasons for that (see the chapters on put selling and similar strategies in the fantastic Expected Returns by Ilmanen). The (small subset of) behavioral finance literature I’m familiar with also points to the possibility effect (or lottery ticket effect) for low-probability events which should result in the same observation (see for example Kahneman). In any case even with a mathematical model, assumptions are made. They may or may not reflect reality. Biases occur then.
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