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4 comments, sorted by Click to highlight new comments since: Today at 7:25 PM

Recently I saw that Hypermind is offering a prediction market on which threshold BTC will hit first: $40k or $60k? You can find the market on this list.

I find this funny because for this kind of question it's going to be a very good approximation to assume BTC is a martingale, and then the optional stopping theorem gives the answer to the question immediately: if BTC is currently priced at $40k < X < $60k then the probability of hitting $40k first is ($60k - X)/($20k). Since BTC itself is going to be priced much more efficiently than this small volume prediction market, the prediction market adds no additional useful information.

The market currently seems to have a bit of a long shot bias: as of the writing of this post BTC is trading at $41.85k which is consistent with 9.25% chances of hitting $60k first, but the prediction market is pricing this at 12.4%. Anyone have any ideas on the reasons behind this?

Ln (41.85/40) / ln (60/40) = 11.2%

It's not the logarithm of the BTC price that is a martingale, it's the BTC price itself, under a risk-neutral measure if that makes you more comfortable (since BTC derivatives would be priced by the same risk-neutral measure pricing BTC itself).

[+][comment deleted]2y10