The crown prince has made the Aramco initial public listing (IPO) the centrepiece of his plan to diversify the Kingdom's economy away from its dependence on oil production by using the $US25.6 billion ($A37.2 billion) raised to develop other sectors.

But that was well below the crown prince's plan announced in 2016 which called for raising as much as $US100 billion via international and domestic listings of a five per cent stake in Aramco.

Bernstein analysts initiated Aramco with an "underperform" rating, estimating its value about $US1.36 trillion.

This compares with US energy giant Exxon Mobil's valuation of less than $US300 billion.

"Saudi Aramco is the largest, most profitable oil company in the world - but size is not everything," they wrote, flagging the risk of slow net income growth if oil prices stay flat.

Bernstein's note said Saudi Arabian Oil Co (Aramco) should trade at a discount rather than premium to international oil majors, with corporate governance "the key risk for investors" as Saudi Arabia will own more than 98 per cent of the company.

"A valuation discount to western oil majors seems warranted," Bernstein said of Aramco, whose shares gained the maximum 10 per cent allowed by the Riyadh exchange on their Wednesday debut.

They hit 38.7 riyals ($US10.32 or $A14.99) on Thursday before easing to 37.5 riyals, putting its market value at $US2 trillion.

Aramco has become the world's biggest IPO, topping the $US25 billion 2014 listing of China's Alibaba despite limited interest from foreign investors leading it to cancel roadshows in New York and London.

It opted instead to sell just a 1.5 per cent stake in Riyadh and rely mainly on domestic and regional buyers.

Some analysts said there could be a lag before the Aramco price settles and some investors take profits from the IPO.

Australian Associated Press