Delta Hedging

Delta hedging means taking a position in the underlying asset that offsets the delta of an option position, so that small moves in the underlying have little effect on total profit or loss. A trader who is long calls with a combined delta of 300 shares can short 300 shares to become delta neutral. Market makers delta hedge almost everything they trade, and volatility traders use it to isolate the part of an option's value that depends on volatility rather than direction.

The basic mechanics#

shares to hedge = minus (option delta × 100 × number of contracts)

Why the hedge does not stay neutral#

Delta changes constantly:

• Price moves change delta through Gamma.
• Time passing changes delta through charm.
• Volatility changes change delta through vanna. See Charm, Vanna and Volga.

A hedge set in the morning may be far from neutral by the afternoon. Traders rehedge periodically, buying or selling the underlying to bring delta back to zero.

Long gamma hedging vs short gamma hedging#

Long gamma hedgers naturally trade against the market and lock in small gains on each rehedge; this is Gamma Scalping. Short gamma hedgers must chase the market, buying after rises and selling after falls, which costs them money. They are compensated by the theta they collect.

How often to rehedge#

More frequent rehedging tracks the theory better but costs more in spreads and commissions. See Transaction Costs.

What determines profit on a hedged option#

The Black Scholes model assumes continuous hedging. Under its assumptions, a delta hedged option earns or loses based on the difference between actual (realised) volatility and the implied volatility paid:

• Bought options at 20% implied volatility, market moves at 30% realised: hedging gains exceed theta paid; profit.
• Bought at 20%, market moves at 12% realised: theta exceeds hedging gains; loss.

This is the foundation of volatility trading. See Implied Volatility (IV), Historical and Realized Volatility and Volatility Trading.

Who delta hedges#

• Market makers hedge almost every trade to stay neutral and earn the spread. See Market Making.
• Banks hedge options sold to clients, including structured products.
• Volatility traders hedge to isolate volatility exposure.
• Funds hedge equity exposure in convertible bond arbitrage and similar strategies.

Aggregate dealer hedging can affect markets. When dealers are short gamma, their hedging adds to moves; when long gamma, it dampens them. See Dealer Gamma Exposure.

Limits of delta hedging#

• Gap risk: prices can jump overnight, past any hedge.
• Costs: frequent rehedging adds up.
• Model error: delta depends on the volatility assumption, so the hedge ratio can be wrong.
• Liquidity: hedging large positions can move the market. See Market Impact.

Common mistakes#

• Hedging once and forgetting.
• Ignoring rehedging costs in strategy planning.
• Thinking a delta neutral position has no risk. Gamma, vega and gap risk remain.

Frequently asked questions#

What is delta hedging?#

Offsetting the delta of an option position with an opposite position in the underlying, so small price moves have little net effect.

How often should you rehedge?#

It depends on gamma, volatility and costs. Traders rehedge at fixed times or when delta moves outside a set band.

Does delta hedging remove all risk?#

No. It removes small directional risk, but gamma, vega, gap moves and costs still affect profit or loss.

Next, see how long gamma traders profit from rehedging in Gamma Scalping.