Shares of financial-technology (fintech) company Shift4 Payments (FOUR 0.22%) suddenly skyrocketed on Thursday after a rumor surfaced that it's potentially an acquisition target for Global Payments (GPN -0.05%). As of 3:45 p.m. ET, Shift4 stock was up 6%, but it had been up by as much as 13% right after the news broke. For its part, Global Payments stock was down about 4%.

Is Shift4 actually for sale?

According to a Bloomberg article today, Global Payments is thinking about buying Shift4 Payments. Bloomberg cited anonymous "people with knowledge of the matter."

Considering that it's trading at one of its cheapest valuations ever, Shift4 might be worth considerably more in an acquisition scenario, which is why the stock is up today on the rumor -- investors want to get out in front of a potential deal.

In November, Shift4's CEO Jared Isaacman surprised investors by saying, "We are actively exploring strategic opportunities and alternatives that will reduce distractions and serve our company, employees and shareholders best." This was in the context of the struggles of being a public company and suggests that the company is looking for a buyer.

Therefore, the still unconfirmed rumor from Bloomberg could indeed be legitimate.

What should shareholders do now?

For Shift4's shareholders, I believe there's a straightforward course of action: Keep holding. If Global Payments acquires the company, it will likely be at a premium to today's price. And if Shift4 stays independent, I believe it has a path to delivering strong stock returns.

The course of action for Global Payments' shareholders is more complex right now. Acquisitions are notoriously tricky to pull off. And until more details emerge, investors can't know if Global Payments is getting a good enough deal on Shift4 or how the two companies would work together to create shareholder value.

In the end, Global Payments' shareholders should probably sit tight and wait as well. But if I were a shareholder, I'd be intently watching out for the details of the potential transaction to know if this was a stock that I still wanted to own for the long haul.