Delta Hedging and Gamma Scalping

Delta hedging offsets an option position’s estimated sensitivity to a small underlying move. Gamma scalping describes rebalancing that hedge as delta changes, commonly around a long-gamma option position. The resulting stock trades can earn money while the overall strategy still loses after option decay and costs.

Establish the initial hedge

Suppose ten standard long calls each have delta 0.50. Their combined delta is 10 × 100 × 0.50 = 500 shares. Selling 500 shares short approximately offsets that local exposure. It does not hedge volatility, time, dividends, jumps or a change in delta.

If the stock rises from $100 to $102 and call delta becomes 0.60, the calls now have 600 shares of delta. Selling another 100 shares restores the approximate hedge. If stock then returns to $100 and delta returns to 0.50 under the stated assumptions, buying back those 100 shares leaves the original 500-share short.

The rebalance ledger

If the calls lose $260 over the round trip and all hedge costs total $20, the combined result over that interval is −$80, assuming the original 500-share hedge has no price P/L because stock returns to $100. Borrow and financing would further change it if not included in the cost figure. The $200 stock gain alone is not the strategy return.

Gamma and theta interact

Long conventional options generally provide positive gamma at a premium and often negative theta. Enough realized movement, captured at suitable hedge times, may offset that carrying cost; insufficient movement may not. Short gamma reverses the typical rebalance direction, buying after rises and selling after falls, while often collecting time decay.

Actual P/L depends on where gamma is concentrated, the price path, implied-volatility changes and hedge timing. A simple comparison of annualized IV and historical realized volatility cannot reproduce all those effects.

Discrete trading leaves residual risk

Continuous hedging without costs is a model idealization. Real markets have spreads, gaps, halts, quantity limits and borrow costs. Hedging more often can reduce some exposure while increasing trading costs. Hedging less often leaves larger directional risk between adjustments.

Specify the instrument, rebalance threshold, session coverage and funding assumptions before testing a hedge. Record option and stock cash flows together, and reprice large shocks rather than extrapolating a constant gamma. Delta neutrality is a local description of a moment, not a promise of a market-neutral outcome.