Is there any model to decide an optimum price to do the rehedging when you are gamma trading? for example, something like getting the daily swings of past 30 days, using GARCH, etc...

If transaction costs were zero you would hedge every second. So discrete hedging is a consequence of transaction costs, including illiquidity.Discrete hedging leads to taking on market risk, so you need to know how much you care about market risk.So the question is one of transaction costs vs risk preferences. See Hodges and Neuberger 1992 for the original work on this. Wilmott "Derivatives" also has a good chapter on this subject.

Isn't that I would try to sell at the highest and then buy at the lowest, if I could predict correctly, but not trying to rehedge every second, even in absence of transaction cost?

if you are "predicting" then you are not really hedging, you are trading directionally.hedging is about minimizing the risk in a position, not necessarily profitably scalping gamma.

It's not too hard to design high-frequency trend trading systems that break even after spreads and commissions. Instead of buying every uptick, and selling every downtick - which would run up about 10 million spread-sized losses in 30 minutes - you develop some mechanical rules for indentifying microtrends.In most situations in the S&P futures, for instance, an uptick at 945.25 will be followed by a downtick at 945.00, where the spread is frozen at this awkward quarter for some fleeting moment. Generally, as a trend piker, you don't want to buy the until the offer races down to 1 last contract, and you are sure it is about to be the bid.I imagine that giving yourself a gamma exposure is, from a mathematical point of view, the same as tweaking the probability the offer is about to become the bid, since you will lose money in the option position. Or, you just increase your utility for breaking even or something. If I had ever hedged an option, I might know something.MP

There's a large area of psychological quicksand right in the middle of the activity known as "gamma scalping". Beware!What I mean is this. A trader with a long gamma long delta position will tell long stories in the pub about his great trading if the share price goes up. The same trader will just quietly allow his delta position to disappear - absorbed in the quicksand of gamma - if the share price goes down. Of course, the cost of doing this is theta.This trader will not just delude his drinking pals about his ability to trade direction; he will also delude himself . Good practice is to set up a seperate directional trading account for traders to do their "gamma scalping" in. This involves a small amount of adminstrative time and effort. However, at the end of the year it is interesting to look at the PnLs of these kinds of accounts. In my experience, very few traders make money at this activity. Almost none make anything like the money that they believe. The ones that do make money this way should be given a big trading limit and moved onto the directional trading prop desk.

I have this fantasy, Johnny, of buying some long option on the cheap, then putting in a series of limit sell orders to hedge it perfectly, and capture vega contraction, as the market rises.Contrary to quicksand, this notion of hedging a long option sounds like walking on the moon! Until you run out of oxygen...MP

Drowing in quicksand or suffocating on the moon? To be honest, they sound pretty similar fates to me, although I guess you would have a better view on the moon.Anyway, my point was about self-delusion. Perhaps you could think of another example in finance?