Since crypto traders have already invented the perpetual futures contract, I'm surprised they haven't taken a stab at the perpetual option, which is pretty theoretically well-studied (and even has a closed-form price solution!)
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... think of them as a very short maturity option (e.g. 8 hours) which automatically rolls into a new option at the same strike. But they are still annoying because you need to pick a strike, so to maintain constant-ish gamma you need to keep rolling up the strike chain.
An attempt to fix /that/ is power perpetuals -- perpetual swaps which track the squared price of the underlying. They have constant gamma and a delta which varies with price. The delta can be dynamically hedged with a 2x short in perpetual swaps to get pure gamma exposure.
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Everyone already linked to the Paradigm 'Everlasting Options' paper so I won't bother, it's only interesting from a theoretical perspective imo. But worth looking up their paper on power perpetuals.
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