I know that while major stock markets are closed, many instruments continue trading overnight. I imagine that some of these instruments track the S&P 500. Is there some easy way to follow these? I don't want to trade overnight, I just wish I could see how those markets move at any given time.
My original answer contained a fundamental error: it turns out that it is not true that any exchange can create its own product to track any underlying index. If the underlying index is copyrighted (such as the S&P indices, Russell indices, Dow Jones indices, etc.) then the exchange must enter into a licensing agreement (usually exclusive) with the copyright holder in order to use the index's formula (and name). Without such a license the exchange would only be able to approximate the underlying index, and I don't think that happens very much (because how would you market such a product?).
The CME offers several futures (and other derivatives) whose face value is equivalent to some multiple of the S&P500's value on the date when the product expires. When such a product is actively traded, it may serve as a reasonable indicator of the "market"'s expectation of the S&P500's future value.
So, you could pay attention to the front month of the CME's S&P 500 Mini future, which trades from 17:00-16:00 Chicago time, Sunday night through Friday afternoon. But remember that the prices quoted there are
- an obscure multiple of the S&P 500's actual value (you need to read the documentation to learn what that multiple is, but if you only care about percent change then you might not care)
- what the market expects the S&P 500's value to be at expiration of the current contract (typically on the 15th of each month), meaning that on the 16th of any month that price may have very little to do with the current underlying index value
As another example, if you care about the Russell 2000 index, until 2017 the ICE Exchange happened to hold the license for its derivatives. They traded from 20:00-17:30 New York time, Sunday night through Friday afternoon. But in mid-2017 CME bought that license as well, so now you'll want to track it here.
Moral: There's almost always some "after hours" product out there tracking whatever index you care about, but you may have to do some digging to find it, and it might not be all that useful for your specific purpose.