By Jamie McGeever

A look at the day ahead in Asian markets from Jamie McGeever.

Global trading volumes return to more normal levels on Tuesday as U.S. and UK markets re-open after their one-day holidays, with optimism over a U.S. debt ceiling agreement set to support risk assets and lift bond yields and the dollar.

The dollar on Monday held firm around its strongest level in over two months against a basket of major currencies and a six-month peak against the Chinese yuan, and strengthened to a new six-month high against the Japanese yen.

The onshore yuan traded weaker than 7.00 per dollar for the eighth straight day, as markets position for another hike in U.S. interest rates and potential policy easing from Beijing.

The dollar nudged 141 yen before closing slightly lower on the day, with traders' hawkish Fed forecasts relative to the Bank of Japan's policy outlook again keeping dollar bulls on the front foot.

If U.S. implied rates and bond yields rise on Tuesday, there is reason to believe the dollar's recent bull run will continue, especially against currencies in Asia where many central banks have signaled their hiking cycles are over.

More detail and clarity around the tentative agreement in Washington to suspend the $31.4 trillion federal debt ceiling should be forthcoming on Tuesday.

It is still subject to approval in both Houses of Congress but leaders on both sides of the aisle say they are confident it will pass. This should boost markets, but they will soon have to face the prospect of Treasury potentially issuing over $1 trillion in bills in the coming months.

But that is for another day. Relief that an unprecedented and probably catastrophic default will be avoided should still be the overriding emotion for now.

Japan's benchmark Nikkei 225 index rose 1% on Monday to a new 33-year high, while Chinese stocks were mixed and the MSCI Asia ex-Japan and MSCI World indices essentially closed flat.

At the time of writing, U.S. stock futures pointed to gains on Wall Street of up to 0.5% on Tuesday.

The Asian economic calendar on Tuesday is light, with Japanese unemployment figures the only major release due. The unemployment rate, which jumped to 2.8% in March, the highest in over a year, is expected to ease back to 2.7% in April.

Here are three key developments that could provide more direction to markets on Tuesday:

- Japan unemployment (April)

- Fed's Barkin speaks

- Germany state CPI inflation (May)

(By Jamie McGeever; Editing by Deepa Babington)