U.S. stocks rose Wednesday and global oil prices fell in yet another volatile trading session as traders and investors were buffeted by constant headlines about the war in Iran.

News of a 15-point U.S. peace plan proposal sparked hopes early in the day that the Trump administration was moving to end its monthlong war against Iran. Initially, the S&P 500 and the Nasdaq 100 futures rose more than 1%.

But reports that Iran had responded negatively to the proposal briefly knocked index futures off their pre-market highs and lifted oil prices off their morning lows.

Despite the early setback, stocks closed the trading day higher. At 4 p.m. ET, the S&P 500 index was up about 0.4%, the Nasdaq Composite closed 0.7% higher, and the Dow jumped 305 points. The Russell 2000 index of smaller companies rose 1.1%.

The price of U.S. crude oil also traded off its lowest levels of the day and was down only 1.4% to about $90 per barrel by late afternoon. West Texas Intermediate crude oil has soared more than 30% since the start of the war on Feb. 28. The cost per barrel is up 50% since the beginning of the year.

International Brent crude prices traded near breakeven, at around $102 per barrel. The price of heating oil, a proxy for jet fuel, dropped 6%.

The global price of oil directly affects what Americans pay at the gas pump and what it costs them to heat and cool their homes. The average nationwide price of unleaded gas Wednesday was $3.98 per gallon, according to AAA data.

“Markets desperately want to believe in the positive,” UBS Global Wealth Management chief economist Paul Donovan wrote. “Focus on the apparent 15-point US plan to end the war has received more attention than Iranian dismissals of this, or the fact that passage through the Strait of Hormuz is minimal.”

Iran’s response to the U.S. proposal included a list of five conditions for ending the war, according to Iranian state TV, which cited a senior political-security official with knowledge of the details of the proposal.

Pakistan has also offered to mediate talks to end the hostilities, four sources told NBC News. A Persian Gulf official said Pakistan had been passing messages between the two countries for the past two days.

An in-person meeting between the U.S. and Iran could be held in the coming days, two sources added.

But President Donald Trump has continued to give conflicting signals.

On March 16, Trump said he was delaying his scheduled visit to China “by a month or so” to monitor the war. On Monday, he said the Strait of Hormuz would be “open very soon.”

And on Tuesday, Trump told reporters in the Oval Office, “This war has been won.” At the same time, the U.S. is sending more than 1,000 additional troops to the Middle East, sources said.

A motorist drives past a sign displaying prices at a gas station in Oakland, Calif., on Tuesday.Godofredo A. Vásquez / AP

Since the war started, the market has experienced several days like this, when markets are whipsawed by constant back-and-forth comments.

“There’s really no way to know at this point what the facts are regarding the state of negotiations, as neither side has any real incentive to conduct talks via the press, so expect more whipsaw action as things continue to progress,” analysts at Bespoke Investment Group wrote in a client note.

They added that the “ongoing tensions continue to support higher prices [and] stoke inflation concerns” and are likely to cause central banks to remain on hold, rather than cut rates.

On the contrary, traders believe the European Central Bank and the Bank of England will both raise interest rates.

“Uncertainty remains high,” analysts at ING wrote in a note Wednesday morning. “Overall, volatility remains elevated and a geopolitical risk premium persists.”

In the 18 trading sessions since the war began, U.S. oil prices have closed down only five times. Likewise, over the same period, the S&P 500 has closed higher only seven times. Three of those higher closes were only fractional.

After Wednesday’s close, the Nasdaq was down nearly 6% for the year, while the S&P 500 was on track for a 3.5% loss so far. The majority of those losses were concentrated in the weeks since the war began.

Meanwhile, the Strait of Hormuz, through which 20% of the world’s oil supply typically passes, has remained at a near standstill since the war began.

On Monday, just five ships passed through the strait, according to data compiled by S&P Global Market Intelligence. On Tuesday, the total was six. On many days since the war started, not a single ship has passed through.

However, some of the ships passing through the strait have taken an unusual course that put them close to the Iranian coastline, potentially signaling that Tehran was keeping a tight grip on traffic flows. Two Indian ships were granted passage Tuesday after a deal with Iran, Bloomberg News reported. The Iranian navy also guided the ships.

Otherwise, hundreds of other ships loaded up with cargo, oil and liquefied natural gas remain stuck.