Options Hedging
Delta hedging
An option position has directional exposure you usually did not want. Neutralise it by holding of the underlying.
Sell 100 calls with delta 0.4 and you are short 40 deltas; buy 40 shares and the position is neutral to small moves.
Then move the delta without touching the position size, which is what gamma does to you between rebalances. The hedge that was right a moment ago is now wrong by the difference, and closing that gap repeatedly is the job.
The complication is that delta changes as the underlying moves, at a rate given by gamma. So the hedge is not a single trade, it is a continuous process.
The frequency decision
Black-Scholes assumes continuous, costless rebalancing. Reality offers neither, and choosing how often to rebalance is a real optimisation.
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