With days before they are due to expire, the contracts have lost as much as a fifth of their value, suggesting that professional investors have missed out on the leap in prices during most of last year.
The first monthly Bitcoin future is due to expire next week, on January 17.
At around US$16,000, the levels they were trading at on Friday, the futures have lost almost 20 per cent from their peak, and over 15 per cent from the first day of trading, when they closed at US$18,500.
CBOE's Bitcoin futures are linked to the price on Gemini, an online-exchange operated by Tyler and Cameron Winklevoss, the twin brothers who own more than $1bn worth of the digital currency, and the price of the contracts mirror that of Bitcoin itself.
Since the futures began trading, Bitcoin has peaked and then reversed some of its exceptional price rises, meaning that while many early owners are sitting on seismic gains, the professional investors who bought up futures contracts last month hoping for the party to continue have largely lost out.
The losses, as well as controversies over how regulators have approved the futures contracts, threatens to dampen professional enthusiasm about Bitcoin.
Last week, the US derivatives regulator, the Commodity Futures Trading Commission, said it would assess the "self-certification" regime that allowed the CBOE and the Chicago Mercantile Exchange to launch Bitcoin futures, after critics said it should have consulted the market.
Major banks have said the watchdog approved the launches too easily and that there was a lack of transparency about how the contracts would work.
Last week both the US Securities and Exchange Commission and North American Securities Administrators Association (NASAA) warned about the dangers of cryptocurrencies, including futures contracts linked to the digital currency.
NASAA said there was a "high risk of fraud" and that the coins had an "unproven track record", while the SEC said several Initial Coin Offerings, cryptocurrency-based crowdfunding schemes, are not following securities laws.
Bitcoin's price has fallen from a high of $20,000 to as low as $12,000 in recent weeks as rival cryptocurrencies have gathered steam, although it was given a boost when it emerged the Silicon Valley venture capitalist Peter Thiel had placed a major bet on its future by investing.