I was told that we cannot predict the market movement, but we can still predict the volatility of the market, if so, can we profit from the prediction of volatility ? Thanks.

Prediction is futile...learn to READ the mkts signals and then you'll be a happy man. Put ego aside and learn the language of the numbers.

Look up GARCH and its variants. It is well known that volatility tends to cluster. The only issue is direction is much less predictable then the squared component of gain. That being said, I'm wondering if jacksmith is being paid to ask all these contentious questions, since he doesn't seem too interested in actually following up, nor learning from any of the replies.

You can trade options to be long or short volatility, or you can trade the VIX itself. As for the prediction part ....

I've attempted using GARCH to do some basic volatility forecasting. I find that you have to incorporate various seasonal functions into your model, because the standard GARCH models decay in various situations that don't seem intuitive. But, as it stands, garch is the default intro to vol forecasting.

I apologize for bumping an old thread, i.e. if it's a faux pas around here, but anyhow to answer your question simply put yes can you trade "volatility". Strictly speaking, if you're looking to trade realized volatility you would probably want to look into trading a variance swap. However, the problem with that is most retail investors, which I'm assuming you are, do not have access to such instruments. Although, you can do a static replication of a variance swap with vanilla options (I suspect the cost may be high though). In the retail scheme, what seems a bit more accessible would be actually trading the difference between realized and implied volatility. You could probably do this by just gamma scalping (i.e. dynamically delta hedging the underlyer), the gamma moves would offset your theta losses. Depending on what your transaction costs are and the amount of haircut you have, this could be highly feasible. Hope that helped!

If we can predict volatility, can we profit from it ? Of course you can. However lets first deal with the semantics. When entering a trade you are predicting - predicting price will go up if you bought or predicting that price will go down if you sold. You could also say anticipating, expecting, etc instead of predicting. And to say just react or just read the market is also predicting. Entering a trade is a prediction that it will be successful. Lets move to a good example. NG on Friday (Sep 11 2009), 9am to 2.30pm, had 11 and half gyrations, thats 23 swings of minimum 35 points. The total offered was 2275 points, a mean average of 98 points per swing. Bottom line: making yourself rich is a choice.