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Stock markets gained on Tuesday after China said it would scrap its COVID-19 quarantine rule for inbound travellers - a major step in reopening its borders.

MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.6%, outperforming an index of global shares, which rose 0.2%. China's bluechip gained 1%.

The pan-European STOXX 600 index rose 0.5%, tracking the rally in Asia, a small gain against the nearly 12% it has lost this year, as central banks' aggressive monetary policy tightening has hit European equities hard.

U.S. stock futures, the S&P 500 e-minis, climbed 0.7%, indicating the market is set to rise as traders return to their terminals on Tuesday after the Christmas holiday.

Markets in some regions including London, Dublin, Hong Kong and Australia remain shut.

The value of bonds fell as yields, which move inversely to price, hit nine-week highs on Tuesday, with German two-year yields at their highest since 2008 to trade around 2.489%, while Italian bond yields rose 11 basis points to 4.622%.

European bond markets have yet to reach peak rates, with the European Central Bank (ECB) lagging behind the U.S. Federal Reserve's jumbo rate increases, according to Florian Ielpo, head of macro at Lombard Odier Investment Managers.

The broader picture looks bullish, he said, pointing to prices on credit spreads and in broader derivatives markets. The, often seen as a gauge of risk aversion, has fallen 35% since the beginning of October, as investors have grown more confident about inflation having peaked.

"What we are seeing today, with a China rally and bullish prices in commodities futures, is what played out in the summer of 2008 and it looks to us like an end-of-a-cycle moment," Ielpo said.

"With a total decline of around 20% this year, it will take a minor miracle for 2022 to not be the weakest year for global stock markets since the financial crisis of 2008," said Lara Mohtadi, an analyst at SEB Bank.

"Last week we also saw the biggest rise in U.S. 10-year yields since April and on Friday trading ended at 3.75%," she said.

The yield on two-year Japanese government bonds (JGBs) on Tuesday jumped to its highest in more than seven-and-a-half years, as an auction for the notes with the same maturity received relatively weak demand.

The dollar fell 0.1% against a basket of major currencies. The euro rose about 0.25% versus the dollar to $1.066.

Commodity currencies such as the New Zealand and Australian dollars also moved higher.

Oil prices ticked up on thin trade, on concerns that winter storms across the United States were affecting logistics and production of petroleum products and shale oil.

Brent crude was up 0.9% at $84.68 a barrel, while U.S. West Texas Intermediate crude was also up 0.8% at $80.22 a barrel

U.S. Treasuries will resume trading on Tuesday after a public holiday on Monday. The benchmark 10-year yield climbed the most last week since early April, ending around 3.75%.

The two-year JGB yield rose to as high as 0.040%, its highest since March 2015, before falling to 0.030%.

Analysts from Citi flagged upside risk in a report on Friday that the Fed's policy interest rate could reach 5.25% to 5.50% by the end of 2023.

Their forecast was based largely on expectations that the labour market would keep adding jobs in the first months of 2023 despite already being very tight, which would put further upward pressure on wages and non-shelter service prices, thereby requiring the Fed to raise rates more quickly.