How can someone in the US trade on the london, HK, Tokyo, Dubai and of course Shanghai markets?

All the online stockbroker sites seem to only deal with NASDEQ stocks from 9:30 am to 4:00 PM. But what about the rest of the world. I know Shanghai is the second largest stock exchange in the world. I know Japan is the second largest economy in the world too so the Nikkei must be pretty big too. How can I start playing those markets? I know I am just a noob right now but the US alone bores me especially when I am up at night and forex is a little too dangerous for noobs.

Simple, sign up with brokers located in those cities.

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