Rebalancing an option hedge over time

Explain how dynamic hedging of an option position is carried out.

Hold the opposite of the option's delta in the underlying and keep adjusting it as the price and time change. Delta moves with gamma, so the hedge is rebalanced periodically or when delta drifts beyond a tolerance. More frequent rebalancing reduces hedging error but raises transaction costs; the hedge also relies on the chosen volatility, and its P&L reflects the gap between realised and implied volatility. Gamma and vega can be hedged with other options.