Shares jumped in trading to reach up to 38.60 Saudi riyals, or $10.29 before noon, three hours before trading closes.
Aramco has sold a 1.5% share to mostly Saudi investors and local Saudi Gulf-based funds.
With gains made from just two day of trading, Aramco sits comfortably ahead of the world's largest companies, including Apple, the second largest company in the world valued at $1.19 trillion.
Crown Prince Mohammed bin Salman is the architect of the effort to list Aramco, touting it as a way to raise capital for the kingdom's sovereign wealth fund, which would then develop new cities and lucrative projects across the country that create jobs for young Saudis.
He had sought a $2 trillion valuation for Aramco when he first announced in 2015 plans to sell a sliver of the state-owned company.
International investors, however, thought the price was too high, given the relatively lower price of oil, climate change concerns and geopolitical risks associated with Aramco. The company's main crude oil processing facility and another site were targeted by missiles and drones in September, knocking out more than half of Saudi production for a while. The kingdom and the U.S. have blamed the attack on rival Iran, which denies involvement.
In the lead-up to the flotation, there had been a strong push for Saudis, including princes and businessmen, to contribute to what's seen locally as a moment of national pride, and even duty. Gulf-based funds from allied countries also contributed to the IPO.
At a ceremony Wednesday for the start of trading, Aramco Chairman Yasir Al-Rumayyan, described the sale as "a proud and historic moment for Saudi Aramco and our majority shareholder, the kingdom."