By the FinLingo Team | Capital markets practitioner, front office experience at a major European investment bank. FinLingo covers 342 lessons from bonds to exotic derivatives. About · Last updated:
Delta hedging is the process of eliminating directional risk from an options position by taking an offsetting position in the underlying asset. If you are long a call option that gains value when the stock rises, you sell enough shares to neutralise that exposure. The result is a position that does not care which direction the stock moves — at least for small moves.
Delta tells you how many shares to trade. A call with delta 0.52 means the option moves approximately $0.52 for every $1 move in the stock. To hedge 100,000 calls, you sell 52,000 shares. The combined position — long calls, short shares — is delta-neutral. This is the most fundamental risk management technique on any options desk.
Delta is not constant. As the stock price changes, delta changes too — this sensitivity is called gamma. A position that is perfectly hedged at $100 develops directional exposure as the stock moves to $105 or $95. The higher the gamma, the faster delta changes, and the more frequently the trader must rebalance. Near expiry, ATM gamma explodes, and rebalancing becomes a continuous battle.
In theory, continuous hedging perfectly replicates the option. In practice, three frictions make it imperfect. First, every rebalancing trade incurs a bid-ask spread. Hedge 50 times a day and the spread adds up. Second, large positions create market impact — your own trading moves the price against you. Third, hedging is discrete, not continuous. You hedge every hour or when delta drifts by 0.01, not continuously. This discretisation introduces tracking error.
The key equation: P&L of a delta-hedged long option position depends on realised volatility versus implied volatility. If the stock moves more than expected (realised vol exceeds implied), gamma rebalancing profits exceed theta decay — the position makes money. If the stock moves less than expected, theta bleeds away more than gamma generates. This is the foundation of volatility trading.
Delta hedging works by taking an offsetting position in the underlying asset to neutralise directional exposure. If you are long a call with delta 0.6, you sell 60 shares per contract. As the stock moves, delta changes (gamma), so you must continuously rebalance by buying or selling additional shares to maintain neutrality.
Three reasons: bid-ask spreads on every rebalancing trade accumulate costs, large positions create market impact that moves prices against you, and real-world hedging is discrete (hourly or threshold-based) rather than the continuous hedging assumed by Black-Scholes. These frictions mean the actual hedging cost always exceeds the theoretical price.
The spread between realised volatility and implied volatility. If realised vol exceeds implied, the gains from gamma rebalancing (buying low, selling high as the stock oscillates) exceed the daily time decay (theta). If realised vol is lower than implied, theta bleeds more than gamma generates, and the hedged position loses money.
FinLingo covers the Greeks and delta hedging in Level 3 — 10 units on all five Greeks plus practical hedging. Level 1 is free.
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