bitfinex.com deals in bitcoin futures, not options like CALLs and PUTs. Like on the stock Apple, I can buy a CALL at the strike price of $110 that expires on January 9th for $131
http://finance.yahoo.com/q?s=AAPL150109C00110000. If the price of Apple goes up above $111.31 before the expiration date you can make money and only risk $131. If I want to protect the Apple shares I own, I can buy a PUT at strike price $100 that expires January 9th for only $14 that will have value if Apple stock drops below $99.86
http://finance.yahoo.com/q?s=AAPL150109P00100000. Thats very cheap insurance for a 10% drop.
You can do all kinds of crazy margin trading on Finex already and even bet with binary options on various shady sites. You can see what this does to the price when you take a lot at Finex: Candles going all the way through to $100, 10k of Bitcoins being sold because of a cascade of margin-calls. People get wiped out there. I wouldn't exactly call this stabilization.