The problem is that the volatility of BTC should be priced off tail risk more than gaussian drift, and that's not a rigorous part of the theory. Black-Scholes certainly doesn't characterize the tails very well.
Nice comment, you seem like you know your stuff. My opinion is without fundamentals or historical or correlated assets here you can't price tail risk beyond throwing a dart. Look at the Futures margin reqs, it's like 40%. A ridiculously high number and that's probably still a compromise because they halt trading for the day around 20%, otherwise I imagine there would be almost no margin given. Price of tail risk is not being priced.