I've said a couple of times that these [ bitcoin-dependent ] businesses and their investors should go together to form a BTC stabilization fund. Not to decide the price range, but to keep manipulators from destroying bitcoins utility by manipulating these violent price swings.
AFAIK there are no such funds for ordinary stocks. I suppose that any such fund would quickly be exausted by traders. It would act as a dumb trader who keeps buying when the market wants to go down, and starts selling as soon as it wants to go up. Once it runs out of money, the price would again swing as before.
Central bankers can in principle stabilize the purchasing power of their currency because they don't have to buy or sell it, they can create it or sequester it by fiat. But when they try to stabilize its exchange rate against foreign currencies, they too will be acting like the dumb trader above, and they too often go bankrupt in the process -- for no lasting result.