Global oil stockpiles 'scarily thin': World's largest oil company. Global oil stockpiles are now “scarily thin”, chief executive of the world's largest oil company, Saudi Aramco, said on Monday. Amin Nasser warned that rebuilding depleted inventories could take up to two years. "The system is already straining," Nasser told Energy Intelligence Forum in London. Yemen's Iran-aligned Houthis recently attacked a facility of Saudi Aramco in Saudi Arabia.