(Corrects typo in paragraph five)

By Anna Szymanski

June 16 (Reuters) - What matters in U.S. and global markets today

By Anna Szymanski, Editor-in-Charge, Reuters Open Interest

The global stock rally triggered by the preliminary U.S.-Iran deal seemed to moderate on Tuesday as markets awaited more details on its terms and looked for signs that it would lead to a meaningful increase in tanker traffic through the Strait of Hormuz.

Attention was also fixed on central banks on Tuesday as the Reserve Bank of Australia and the Bank of Japan kicked off the week's busy calendar for monetary policymakers. The BOJ delivered an expected quarter-point rate hike to 1%, a 31-year high.

I'll get into that and more below.

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CENTRAL BANKS TAKE THE STAGE

Despite President Donald Trump's comments on Monday that oil tankers were exiting the Strait of Hormuz, there were no significant tanker crossings visible in vessel-tracking data on Monday - although ships continue to move along Oman's coast under the watch of the U.S. Navy.

Brent crude moved down further on Tuesday, having slid some 5% on Monday, but held above $80 per barrel. Meanwhile, global shares extended their gains as major Asian indexes edged up and European shares opened higher. Wall Street futures were broadly flat before the bell.

It's still early days, and Trump said on Monday that the text of the deal would be released after its formal signing on Friday. Meanwhile, fighting between Israel and Hezbollah in Lebanon eased on Monday.

Moving to central banks, the BOJ's expected rate hike to 1% represented another step in the normalization of the country's monetary policy as it sought to tamp down price pressures that were exacerbated by the Iran war-driven energy shock. Speaking on Tuesday, BOJ Deputy Governor Shinichi Uchida welcomed the U.S.-Iran memorandum but noted uncertainty on the "pace of improvement" regarding oil flows.

The well-telegraphed move had little impact on the yen, which remained near 160 to the dollar. Any further weakness from here could trigger another bout of government intervention to prop up the currency.

Meanwhile, the Reserve Bank of Australia kept rates unchanged at 4.35%, highlighting the slowing economy, but it also warned that inflation remained too high, meaning it may yet hike rates.

While the Federal Reserve and the Bank of England are expected to leave rates unchanged when they meet on Wednesday and Thursday, respectively, their language will be closely scrutinized as investors assess how the prospect of a resolution to the Iran war could influence their rate paths.

On the tech front, Elon Musk's SpaceX continued to shoot upward after its monster IPO last Friday, having risen more than 19% on Monday. Its moves in premarket trading put it on track to become the world's fifth-largest company, eclipsing $2.7 trillion Amazon.

It's worth considering that more than $1.16 billion of SpaceX shares had exchanged hands as of early this morning. That's several times the trading volumes in Nvidia, Microsoft, Tesla and Apple combined over that period.

Elsewhere, Nvidia on Monday announced a $25 billion U.S. bond issuance, the first time it's tapped debt markets since 2021. While the raise makes the chipmaker the latest in a string of tech heavyweights to raise cash amid the AI bonanza, the catalyst does not appear to be capex funding needs but instead a desire to establish a liquid benchmark for its cost of credit.

Finally, the G7 is currently meeting in the French lakeside resort of Evian-les-Bains to discuss war, global economic imbalances and the rapid rise of AI.

Chart of the day

Some 24% of Americans currently approve ​of President Trump's stewardship over the cost of living, up from 22% a week earlier and 20% a month ago. The share who disapprove has eased to 69% in the latest Reuters/Ipsos poll from 73% a month earlier.

The four-day poll gathered responses before and after Trump announced on Sunday that he and Iranian leaders had agreed to end the war that had pushed gasoline prices sharply higher.

Today's events to watch

-- U.S. May housing starts (8:30 a.m. EDT), May import prices (8:30 a.m. EDT)

-- U.S. 20-year bond auction (1 p.m. EDT)

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