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No, Small Probabilities are Not 'Attractive to Sell': A Comment

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Abstract

Owing to the convexity of the payoff of out-of-the money options, an extremely small probability of a large deviation unseen in past data justifies rationally buying them, or at least justifies excessive caution in not being exposed to them, particularly those options that are extremely nonlinear in response to market movement or changes in implied volatility. One needs, for instance, a minimum of 2000 years of stock market data to assert that some tail options are "expensive." The paper presents errors in Ilmanen (2012), which provides an exhaustive list of all arguments in favor of selling insurance on small probability events. The paper goes beyond Ilmanen (2012) and suggests an approach to analyze the payoff and risks of options based on the nonlinearities in the tails.

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