Trump's vast power to reshape the Fed will be the next major source of uncertainty for markets

President Donald Trump already had ample leeway to reshape the Federal Reserve, with Janet Yellen's term as chair expiring early next year and two key slots on the central bank's board left open after Republicans failed to bring President Barack Obama's longstanding nominees to a vote.

Now, with the sudden resignation of Daniel Tarullo, President Trump pretty much has full reign over the powerful US central bank.

Tarullo was the Fed's point man on regulation, and his announcement came just days after the new administration announced it was ready to tear up the very post-financial-crisis rules that Tarullo, Fed officials, and other regulators have spent years debating and implementing.

Tarullo's term was not due to expire until 2022. He could have, as The New York Times' Binyamin Applebaum tweeted, stayed on to fight against the looming rollback.

But in the end, Tarullo was all too aware that as independent as the Fed likes to think of itself, it is ultimately accountable to Congress and, by the nature of appointments, the president. Why fight a losing battle and then have your name associated with the next financial blowup? One can forgive him for calling it quits after eight years.

That battle will ultimately take place in the realm of politics, not policymaking, as indicated by the pushback Trump is getting from Democrats in addition to many Europeans, who fear deregulation in the US could destabilize their banking systems.

Trump has vowed to do a "big number" on Dodd-Frank, and he placed former Goldman Sachs president Gary Cohn and his recently confirmed Treasury secretary, Steve Mnuchin, also a longtime Goldman banker, in charge of doing the dismantling.

On interest-rate policy, the Fed's board also loses a publicly circumspect but vocal voice calling for a more dovish, pro-employment approach to policy, particularly with inflation hovering below the central bank's target for most of the economic recovery.

The trouble of predicting what a Trump Fed would look like is the same problem with trying to predict anything Trump: It's not really possible. It's clear that one name, that of Kevin Warsh, a Republican former Fed governor, will cross Trump's desk when he turns his attention to the issue of the Fed. It's hard to imagine he has given it much consideration given all the other controversies that have embroiled his first couple of weeks in office, including immigration and foreign relations.

But three open slots are coming up soon, and the vice chairmanship will also be up for grabs.

That list of names just doesn't exist yet. If he listens to the Republican establishment, the list could include conservative economists like Harvard's Greg Mankiw, a former George W. Bush adviser, and Hoover Institution fellow and former Treasury official John Taylor.

If he doesn't, as is often the case, the picks for governors and chair are hard to fathom. Perhaps someone with a bit of television flair, press-conference ready. Jim Cramer? Suze Orman?

This is an opinion column. The thoughts expressed are those of the author.