Traders say future prices are likely to fluctuate, as they do with current share prices on the Nasdaq.
The microblogging site was the second largest internet IPO and stock price soared above the initial asking price in initial days of trading, which caused investors to be skeptical about the true value of the company. It currently is not turning profits, but has potential to create value.
Twitter recently released a new "custom timeline" that's helped media and entertainment outlets better streamline content.
It's also showing potential for greater mobile advertising -- increasingly important given that the number of smartphone users is rising rapidly, expected to more than triple to 5.6 billion subscriptions worldwide by 2019.
Twitter share prices have soared more than 70 percent since its IPO debut, and options to buy the stock gives traders the ability to protect against future price changes.
Twitter's share price dipped in midday trading to $43.70.
The CBOE reported that Twitter options strike prices will be between $35 and $50. It is said that many traders are short selling the stock, meaning the share price is expected to drop. This is the case for a number of Internet companies currently being closely watched.