I am not an Islamic scholar.
I started doing some research on this several months ago, and came to following conclusion.
First point, what is BTC, a currency or commodity? In Islam there should be some solid thing as currency, as gold, silver etc used to be. Even our Pakistan Ruppee has gold behind it (that’s what written on our note, HAMIL E HAZA KO MUTALBA PER ADA KYA JAEGA). BTC does not have any such thing, so It cannot be counted as currency however it can be used as commodity like a product or company share.
According to my study, there are two concepts in Islam:
1- The investment should be made completely in business shares or currency
2- There should be some solid business or work happening behind that share or currency.
To further describe the first point: There are two concepts.
1- Buy with full cash: I want to buy 2 BTC at $2500. So I will pay hard cash, i.e $5000 and buy BTC against it. When the rate increases, I will sell it out. That according to my homework is 100% permissible and Halal.
2- Margin Trading: Buy 1 BTC , pay $100 and remaining is to be paid after 1 month. During one month you find a customer, sale it to him. Then return 2400$ to original owner and keep the profit. That is HARAM and NOT PERMITTED is Islam. It is making profit over something you are not owner of.
Now speaking about point 2:
1- All currencies are being developed and some contracts are being done behind the scene. Based on that, value increases or decreases.
DISCLAIMER: Please do your personal research as well. The above mentioned is my opinion and thinking and it is not a FATWA. If you find out that this is not permitted, do let me know as well because I am not interested in earning HARAM.