Delta hedging is the practice of eliminating directional risk from an options position by taking an offsetting position in the underlying asset. It is the most fundamental risk management technique on any options trading desk, and understanding it is essential to grasping how dealers manage their books in practice.
Every option has a delta that measures its sensitivity to small moves in the underlying price. A call option with a delta of 0.6 will gain approximately $0.60 in value for every $1 rise in the stock. To hedge this exposure, the trader sells 60 shares of the underlying per option contract. The combined position — long the call, short the shares — is now delta-neutral: small moves in the stock produce no net profit or loss.
Put options work symmetrically. A long put with a delta of -0.4 is hedged by buying 40 shares of the underlying. The sign of delta tells you the direction, the magnitude tells you the size of the hedge.
Delta is not constant — it changes as the underlying moves, as time passes, and as implied volatility shifts. The rate at which delta changes with respect to the underlying price is called gamma. A position that is perfectly delta-neutral at $100 will develop directional risk as the stock moves to $102 or $98. This means the trader must continuously rebalance the hedge, buying shares when the stock rises (delta increases) and selling when it falls (delta decreases). This rebalancing process is sometimes called "gamma trading" because the need to rehedge is driven entirely by the position's gamma.
In the theoretical Black-Scholes world, hedging is continuous and costless. In reality, traders face three sources of friction. First, every rebalancing trade incurs a bid-ask spread — the more frequently you hedge, the more spread you pay. Second, large positions create market impact: rebalancing a thousand-lot option position moves the underlying price against you. Third, hedging is discrete rather than continuous. Traders typically rehedge at fixed intervals (every hour, at the close) or when delta drifts beyond a threshold. This discretisation introduces tracking error between the hedge and the option.
The profitability of a delta-hedged long option position depends on the relationship between realised volatility and implied volatility. If realised volatility exceeds the implied volatility at which the option was purchased, the gains from gamma rebalancing (buying low, selling high as the stock oscillates) exceed the daily time decay (theta). This is the principle behind gamma scalping — buying options and profiting from the underlying's actual moves. Conversely, if realised volatility is lower than implied, the theta bleed outweighs the gamma gains, and the hedged position loses money.
On a sell-side derivatives desk, traders rarely hedge continuously. They balance the cost of hedging against the risk of leaving delta unhedged. Common approaches include hedging on a timer (every few hours), hedging when delta exceeds a band, or hedging at the close. The choice depends on the desk's gamma profile, transaction costs, and risk appetite. Market makers with large, diversified books often benefit from natural netting — the delta from one client trade partially offsets another — reducing the frequency of external hedging.
Learn delta hedging interactively with FinLingo's Greeks modules.
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