Oil prices are dropping further, and stocks are rallying worldwide Tuesday on hopes that Israel's war with Iran will not damage the global flow of crude, even if a tentative truce seemed to fray under fire in the morning.

The S&P 500 was 0.7% higher in early trading, following up on even bigger gains for stocks across Europe and Asia, after President Donald Trump said late Monday that Israel and Iran had agreed to a "complete and total ceasefire." The Dow Jones Industrial Average was up 289 points, or 0.7%, as of 9:31 a.m. Eastern time, and the Nasdaq composite was 0.9% higher.