For options trading, it's depends on the level that you're requesting from the broker,
and the securities that you want to trade.

I think it somewhere between $1000 to a few millions (for naked shorts capability)... 

For example:
Want to write a short PUT for SPY?
This week it will be something like this:
1 PUT will need $51,000 as collateral.
10 PUT will need  $510,000.
100 PUT will need $5,100,000.