If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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Yeah, but you wanted "a scenario where everything is happening pre-tax, there are no transaction costs, we're operating in risk-adjusted terms and, to make things simple, the risk-free rate is zero. Moreover, the markets are orderly and liquid." That doesn't describe reality, so describing events in your scenario necessitates a toy model.
In the real world, it is trivial to show how you can lose money even if the EMH is true: you have to pay tax, transaction costs are non-zero, the ex post risk is not known, etc.
There's still a lot of correlation. Selling deep OOM options and then running into unexpected correlation is exactly how LTCM went bust. It's called "picking up pennies in front of a steamroller" for a reason.
Fair point :-) But still, with enough degrees of freedom in the toy model, the task becomes easy and so uninteresting.
I know. Which means you need proper risk management and capitalization. LTCM died because it was overleveraged and could not meet the margin calls. And LTCM relied on hedges, not on diversification.
Since deep OOM options are traded, there are people who write them. Since they are still writing them, it looks like not a bad business :-)