Delta Hedging
A risk management technique that offsets an option's price sensitivity to the underlying asset by holding a position in the underlying equal to the option's delta.
What is Delta Hedging?
Delta hedging is the practice of creating a portfolio that is delta-neutral — insensitive to small price changes in the underlying asset — by offsetting an options position with a position in the underlying stock or futures. Because a call option has a delta between 0 and 1, a market maker who has sold 100 call options with a delta of 0.50 hedges by buying 50 shares (100 × 0.50) of the underlying. As the underlying price moves, the option's delta changes, requiring continuous rebalancing — a process called dynamic delta hedging. The cost of delta hedging (from buying high and selling low as the market moves) is essentially the premium paid for the option's gamma. Delta hedging isolates and monetizes volatility risk.
Example
An options dealer sells 500 at-the-money call contracts (50,000 shares equivalent) with a delta of 0.50, creating short delta exposure of 25,000 shares. To hedge, the dealer buys 25,000 shares of the underlying. As the stock rallies and the call delta rises to 0.60, the dealer buys an additional 5,000 shares to maintain delta neutrality. The rebalancing trades are the practical cost of providing liquidity in options markets.