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Key Takeaways
- Long gamma changes option delta as the underlying moves.
- Hedging long gamma back to zero delta sells shares into a rise and buys them back on the dip, so each completed round trip sells high and buys back lower.
- The completed 100-share trade from $102 to $100 earns $200 gross.
- Total strategy P/L combines option-value changes, share-trading P/L, funding, distributions and fees.
- Judge the trade on the full ledger: share P/L from actual fills plus the options’ value change, funding and fees.
What is gamma scalping?
Gamma scalping is an options strategy that holds a long-gamma option position with an offsetting stock hedge, then buys or sells shares as option delta changes to return toward the target net delta. Each completed hedge round trip captures part of the underlying’s movement, and those share profits have to outweigh the options’ time decay and trading costs.
In the worked call example, an upward move raises delta and requires more short shares. A return to the original price lowers delta and requires buying shares back. Those completed share trades are the scalp, and the options’ own value change settles whether it paid.
Formula
Local gamma contribution to a delta-hedged position ≈ ½ × position gamma × (price change)². Total strategy P/L = option P/L + share P/L + funding and distribution cash flows − fees.- Position gamma is option gamma × signed contracts × multiplier, measured in share-deltas per $1.
- The example’s position gamma is 0.05 × 10 × 100 = 50.
- A $2 move gives a $100 local gamma contribution: ½ × 50 × 2².
- The gamma contribution shows up in the combined position’s value, and a hedge round trip turns it into cash only when it closes, as the $200 trade does after the move up and back.
- Calculate share P/L from the actual inventory, trade prices and ending stock value.
Gamma scalping example: hedging a $2 round trip
A trader holds 10 standard XYZ calls at stock price $100, with quoted delta 0.50 and gamma 0.05. Short 500 shares for zero initial delta. For the worked path, updated call deltas are 0.60 at $102 and 0.50 when the stock returns to $100.
- Initial option share-delta: 10 × 100 × 0.50 = +500; stock hedge −500
- At $102, option share-delta is +600; sell 100 shares to reach −600
- Back at $100, option share-delta is +500; buy 100 shares to return to −500
- Completed incremental stock trade: 100 × ($102 − $100) = +$200
- Over the holding period, the options lose $150 of value and trading and funding costs total $30
- Combined result for that illustration: $200 − $150 − $30 = +$20
The incremental 100-share round trip earns $200 gross and restores the initial −500-share hedge. After the $150 option loss and $30 of costs, the strategy nets $20: the scalp covered the option loss and the costs.
The incremental short-sale round trip earns 100 × ($102 − $100), or $200 gross. The original stock hedge is back at its entry price. The options’ value change over the same stretch is the other half of the result.
How is gamma scalping profit calculated?
Add the options’ P/L to the stock P/L, funding and distribution cash flows, then subtract fees. With a $150 option-value decline and $30 total costs in the extended example, the $200 share result becomes $20 total profit.
The local gamma contribution is one-half position gamma times the squared underlying move. Position gamma of 50 and a $2 move gives $100. This measures curvature in the combined delta-hedged position, and the cash arrives when a hedge round trip closes: the sale at $102 pays only once the buyback at $100 completes it.
How to plan gamma scalping rebalances
Set the target delta and the price, time or delta threshold for each adjustment. Record the option marks, share inventory and execution prices at those points.
Compare implied volatility with the realized path, then evaluate the actual option and hedge cash flows. The options profit calculator shows the options’ value, gamma and theta as price and implied volatility change, the option half of the P/L; log every hedge fill beside it for the share half.
Risks and limitations of gamma scalping
- Make the hedge profits cover theta. A typical long-gamma position has negative theta, so when hedge profits fall short of time decay and other changes in option value, the strategy loses money.
- Track vega alongside the scalp. A fall in implied volatility lowers the options’ value even when the stock moves as hoped.
- Set the rebalancing rule for the path you expect. Frequent hedges add costs, and infrequent hedges leave directional exposure between adjustments.
- Rebalance on moves large enough to clear costs. Spreads and fees on each rebalance come out of the scalp, and on small moves they can absorb it.
- Count profit from closed round trips and option marks. The one-half gamma times move-squared term sizes small moves only, since gamma changes with price and time.
Bottom line
Gamma scalping turns realized price movement into hedge profits that help pay for a long option position’s time decay. Success depends on the realized path, hedge timing, changes in option value and execution costs. Set the rebalancing rule in advance and judge the result from the complete option and stock ledger.
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Sources and Further Reading
How entries are sourced, calculated and updated: editorial methodology.