Mt.Gox, once the world's biggest bitcoin exchange, filed for bankruptcy on Feb. 28, saying it may have lost nearly half a billion dollars worth of the virtual coins due to hacking into its faulty computer system.
There is no obvious mechanism that ensures that bitcoin will achieve that stability, said Wilson and Ursua.
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"For fiat currencies, central banks are tasked specifically with preserving a relatively stable value. To do that, they are able to vary the supply of currency. But bitcoin has no equivalent authority prepared to act to guarantee the stability of its value," they said.
Wide-spread use conceivable
Nevertheless, the bank says bitcoin shows more promise in terms of its payments technology.
"Although it is not yet 'widely' accepted, the ability to pay for goods and services using bitcoin is growing," they said.
"And the fundamental obstacles to bitcoin being used more broadly in the payments system are arguably not insurmountable, though connections with the conventional banking system are ultimately essential to its functioning," they added.
(Read more: Singapore's first bitcoin ATM opens for business)
The absence of derivative markets makes it harder to manage and hedge risk around bitcoin's value, but it is possible to imagine how those could ultimately develop, Wilson and Ursua said.
"On net, more than taking off as a widely-used alternative currency, it is much more plausible that bitcoin eventually has a significant impact in terms of its innovation on payments technology, by forcing existing players to adapt to it or coopt it," they concluded.
—By CNBC's Ansuya Harjani. Follow her on Twitter