I was wondering why options are only traded on exchanges during market hours and not after hours like stocks. Is it a liquidity issue? For the mega cap stocks though, even the options market has a fair amount of liquidity, no?
The US options exchange are generally open only from 9:30 AM to 4:00 PM (4:15 PM for index options). This is written in the exchange rules, which are in turn filed with and enforced by the Securities and Exchange Commission.
The options exchanges also impose rules on their Market Makers to provide liquidity 'continuously' while the options exchange is open for trading.
The Market Makers often trade using a delta-neutral strategy which requires that they hedge any options they buy or sell with the underlying security. If the underlying is illiquid or the spreads are wider, the options market maker will need to quote with wider spreads accordingly. If the spreads are too wide, people would not be interested in buying or selling the options.
Furthermore, if the options market were open later, the Market Makers (and exchanges) would need to employ another shift of staff to be able to allow trading to continue in those extended hours.
Like most things, it is down to demand. If there is sufficient demand, the hours might be extended. CBOE is presently experimenting with Extended Hours Trading of options in some of their proprietary products (VIX, SPX).
I'd guess that it's a liquidity issue. Although there are 3,000+ stocks that offer options (and many ETFs as well), an awful lot of them trade by appointment and have hardly any open interest. Therefore, the return (fees and spreads) isn't worth it to a market maker for the time involved.
And then there's the issue of daily contract exercise. The OCC needs time to collect submitted exercise notices and use their "wheel" each night to apportion assignment notices to brokers so that traders can be notified in a timely fashion. Should they work into the middle of the night to be able do so?
A more facetious answer would be a question like why are banks closed on Sunday? Because they want to be.
As a side note, be aware that you can use after hours trading to lock in gains or cut losses in your option position by utilizing the underlying. Many times I have seen a stock jump a lot on good news and by 9:30 AM when regular trading resumes, the gain is lost. A long call holder is you know what out of luck when that happens.