What delta means
An option's delta (Δ) is the rate of change of the option's price with respect to the underlying asset's price. A call option with delta 0.5 means that for every £1 rise in the stock, the option gains £0.50. Delta ranges from 0 to 1 for calls (and −1 to 0 for puts). At-the-money options have a delta close to 0.5. Deep in-the-money options have delta close to 1 (they behave like the stock). Deep out-of-the-money options have delta close to 0 (they barely move with the stock).
The hedging process
An options market-maker who sells a call option acquires negative delta (the option gains value if the stock rises, which is bad for the seller). To neutralise this, the market-maker buys the underlying stock in proportion to the delta. If the option has delta 0.5 and the contract covers 100 shares, the market-maker buys 50 shares. Now the portfolio is "delta-neutral" — small moves in the stock produce no net P&L. But delta changes as the stock price moves (this rate of change is gamma), so the hedge must be continuously adjusted. This dynamic rebalancing is "delta hedging."
Gamma: the cost of hedging
Gamma (Γ) measures the rate of change of delta. High gamma options (typically near-term, at-the-money) require frequent, large rehedging — every small move in the stock changes delta significantly, forcing the market-maker to trade. This rehedging has a cost (bid-ask spreads, market impact). The option premium charged to the buyer must cover the expected total cost of hedging over the option's life. This is why volatility is so central to options pricing: higher expected volatility = higher expected hedging costs = higher option premium.
Vega and the other Greeks
Delta and gamma address price risk. But options are also sensitive to changes in implied volatility (vega), time decay (theta), and interest rates (rho). A fully hedged options book manages all of these simultaneously. Market-makers typically delta-hedge continuously while managing their aggregate gamma, vega, and theta positions through offsetting options trades with other counterparties. The skill is not eliminating all risk (impossible without infinite transaction costs) but managing risk so that the collected premium more than covers the hedging costs over time.
"Delta hedging converts the directional risk of an option into a pure volatility bet — you profit if realised volatility exceeds what you paid for in implied volatility." — Options trading insight
What this means for you
Delta hedging is the backbone of the $13 trillion global options market. When companies buy equity puts for downside protection, or when pension funds use interest rate swaptions to manage duration, the banks that sell them continuously delta-hedge their resulting exposure. Understanding the hedging dynamics explains why large option expiries ("max pain" and "gamma squeeze" phenomena) can create unusual stock price patterns as market-makers rebalance. It also explains why volatility is so valuable: it's the input that determines the cost of replication.