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I was teaching a class once at the Chicago Board Options Exchange. At the intermission, a student came up to me and asked if I could teach him delta-neutral strategies. I asked why he wanted to learn about them and he replied, "... because that's where the big money is made!"
That statement may or may not be true. Certainly it is possible to make "big money" trading delta-neutral. But the same can be said about lots of different option strategies. Delta-neutral trading is just a different method that enables traders to profit from something that other strategies don't allow for.
Essentially delta-neutral strategies are those where the delta -- that is the directional sensitivity of the trade -- is about zero: it's, well, neutral.
So, how do traders make money if not from the underlying stock moving? With delta-neutral strategies, they profit from the other option-centric risks. Delta-neutral traders are effectively trading time and volatility.
These traders watch the greeks very closely. Gamma, theta and vega are the commodities these guys watch. The positions can be rather complex at times, but they don't have to be. There are plenty of fairly straightforward, delta-neutral trades that are common among retail traders.
Want to learn more? Watch this video Jill Malandrino and I shot at the Nasdaq yesterday.