“The market is so hopeful for a deal that would open the Strait of Hormuz that it doesn’t care about the details and it is willing to trade on hope rather than wait for the outcome,” said Steve Sosnick of Interactive Brokers.

About 10 minutes into trading, the Dow Jones Industrial Average was up 0.3% to 50,735.99.

The broad-based S&P 500 gained 0.6% to 7,516.44, while the tech-rich Nasdaq Composite Index gained 0.8% to 26,552.86.

Optimism about a US-Iran deal has helped lift markets for weeks, leading to numerous records.

Markets are shrugging off Iran’s accusations that the US has breached its ceasefire after overnight US strikes targeting Iranian missile sites.

Despite the strikes, secretary of state Marco Rubio said on Tuesday that a deal remained within reach.

“There were some talks going on in Qatar today, so we’ll see if we can make progress,” Rubio said.

But Sosnick described the market’s default position as bullish, saying, “The stock market has not imposed a penalty for being wrong or for being overenthusiastic.”