In a note on Friday, Lee forecast that the cryptocurrency could rise to $6,000 a coin by the middle of next year.
He said the big driver of this 29% rally through mid-2018 would be greater public awareness of bitcoin as a method of payment and as a store of value like gold. He maintained his 2022 target of $25,000.
"We see bitcoin as gaining from institutional sponsorship, improving transaction platforms and ultimately, greater public adoption," Lee said.
Investors who don't want to buy bitcoins will soon have a way to invest in the cryptocurrency. In July, the Commodity Futures Trading Commission cleared LedgerX, a cryptocurrency-trading platform, to offer bitcoin options by this fall. While also making it easier for investors to bet against bitcoin, Lee sees this as a bullish development because it would increase participation.
Central banks could also jump in. "While one may say this is preposterous to say central banks would own bitcoin — we believe that Central banks would view crypto currencies differently if Bitcoin’s aggregate value exceeded $500 billion," Lee said.
His forecasting model for bitcoin's value is based on Metcalfe's Law, which stipulates that a network's value increases exponentially based on the number of users within it. Lee projected that bitcoin user accounts would grow 50% by 2018.
Technical analysis — traders' use of chart patterns for forecasting — also suggests that bitcoin is set to continue climbing. The cryptocurrency this year broke out of a four-year trading range.
"Short-term traders should be prepared for another volatile consolidation period heading into late August given the XBT is nearing our next resistance levels with daily/short-term momentum becoming overbought," Lee cautioned. Bitcoin has surged about 337% this year.
Lee's year-target for the S&P 500 is 2,275. It's the lowest among strategists at major firms tracked by Bloomberg, and implies that the index would fall about 6% from Friday's opening level.