Analyst Johann Palychata writes in the company's magazine Quintessence that bitcoin's blockchain, the software that allows the digital currency to function, "should be considered as an invention like the steam or combustion engine," that has the potential to transform the world of finance and beyond.
The blockchain is an online ledger of all the bitcoin transactions that take place. It's spread across thousands of computers and servers globally.
It lets people exchange bitcoin by spreading the record of exchanges and ownership history across a wide area. It adds a layer of trust that is essential to bitcoin - everyone can check a coin hasn't been double spent and is actually owned by the person claiming to.
Palychata says that if this type of technology is applied to securities trading - the world of buying and selling company shares - then "existing industry players might be redundant."
If investors can trade shares directly with each other in a system that has a layer of trust built into it then middle men - stock brokers - aren't needed anymore.
That's a huge thing for an investment bank to say, especially one of BNP Paribas' size - it's France's biggest bank.
Most banks have been keen to play down the competition from financial technology, or fintech, startups, saying new technology presents opportunities rather than threats.
Falling technology costs and the disruption that followed the financial crisis of 2008 have lead to a wave of innovation and competition for banks. Bitcoin and the blockchain are some of the most cutting edge financial experiments we've seen.
Banks like Santander and Barclays are investing in and experimenting with financial technology of their own, saying it's a good chance to improve their own services.
But the truth - as Palychata makes clear - is these banks are being forced to innovate. While its unlikely that any one of hundreds of startups currently springing up will replace Santander or Barclays, banks face death by a thousand cuts as startups attack different parts of their businesses from multiple angels. If they don't do something soon it will start to affect the bottom line.
Palychata's scenario of blockchain being applied to stock trading isn't such an outlandish scenario either - US exchange operator Nasdaq is currently experimenting with the blockchain.
That said, Palychata's "redundant" prediction is a worst case scenario. He believes it's more likely that stock broking firms will adopt the blockchain technology to trade among themselves, rather than offer it directly to consumers.
And even if a startup or coder builds a blockchain for trading shares and opens it directly to the public, Palychata thinks the security issues around keeping private keys - the access codes used to get digital assets traded on the blockchain - means current firms could develop a new role as the guardians of these keys.
But the fact that an analyst is using the word "redundant" shows how seriously banks are taking this threat.