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Key Takeaways
- Gamma pinning describes an underlying trading close to an option strike as expiration approaches.
- A delta-hedged long-gamma book sells shares after a rise and buys shares after a fall.
- Near-expiration gamma concentrates around strikes close to the underlying price.
- A pin needs net long-gamma hedgers and hedge orders that are large against the underlying’s liquidity.
- After settlement, map the remaining options and stock positions to identify the next exposure concentrations.
What is gamma pinning?
Gamma pinning is price clustering near an option strike as expiration approaches. It is linked to long-gamma hedging, which opposes price changes: a dealer that holds long options with a delta hedge sells shares as option delta rises and buys them back as delta falls.
Near expiration, gamma concentrates around strikes close to spot. Combine that sensitivity with the signed position size to calculate the resulting hedge orders. Open interest identifies where contracts sit; signed inventory determines whether their hedge trades oppose or reinforce a price move.
Formula
Hedge-share change = −100 × Σ[signed contracts × (new per-share delta − previous per-share delta)]- Use this formula for standard 100-share equity options, with long contract quantities positive and short quantities negative.
- For a small price change, delta change is approximately gamma × underlying price change. Reprice delta for the full move.
- A positive hedge-share change is a purchase; a negative change is a sale.
Gamma pinning example: hedging 8,000 long calls
XYZ starts at $104.60. A dealer holds 8,000 long standard 105 calls with per-share delta 0.48, hedged with short stock. In the next two scenarios, the call delta moves to 0.54 and then 0.42.
- Initial option exposure: 8,000 × 100 × 0.48 = +384,000 shares; stock hedge: −384,000 shares
- At delta 0.54: option exposure is +432,000 shares; sell 48,000 more shares
- At delta 0.42: option exposure is +336,000 shares; buy back 96,000 shares
- Gross hedge turnover: 48,000 sold + 96,000 bought = 144,000 shares
The dealer sells on the first upward delta change and buys on the reversal. Those orders oppose the price moves. Compare their size with trading liquidity near the 105 strike, then recalculate the remaining book after expiration.
These calculations use each scenario’s delta. For a small price change, gamma times that price change estimates delta’s response. For a larger move, reprice each contract and recompute the complete hedge.
How traders assess a potential gamma pin
Use gamma exposure to locate concentrations around spot and compare expirations. Match the exposure to the liquidity of the underlying and the instruments used for the hedge. Follow price, volume and the actual response at each level.
A long vanilla option retains positive gamma on either side of its strike. A portfolio’s net gamma changes with the quantities and sensitivities of all its long and short contracts. Recalculate the whole book when price moves through a strike.
Gamma pinning vs max pain
Max pain selects the price that minimizes aggregate expiration intrinsic value using open interest. Pinning describes observed price clustering and the long-gamma hedging mechanism. Max pain points to a payout-minimizing level and a pin comes from hedge flow, so the two can sit at different strikes.
What changes after expiration
After expiration, remove settled contracts and account for resulting stock positions. Map the remaining book to identify the next exposure concentrations. Carry those levels into the trading plan and compare the planned option position in the options profit calculator.
Limitations of gamma pinning
- Trade a pin with defined risk. Price can settle away from a heavy strike, and the hedging leans against moves only when the hedgers are net long gamma.
- Check the sign before the size. Open interest shows where contracts sit, and if the hedgers at a strike are net short gamma, their trades reinforce moves instead of opposing them.
- Measure hedge size against liquidity. Hedge orders that are small against trading in the underlying have little effect, whatever the open interest.
- Reprice every contract on a larger move; gamma sizes delta’s response only for small ones.
- Remap the book after settlement, since the expiring exposure and its pull disappear with it.
Bottom line
Into expiration, long-gamma hedging sells every rise and buys every dip around a heavy strike such as 105, and that two-way hedging is what holds a pin. Check the signed exposure at nearby strikes and the hedge size against liquidity before you trade the pin, then remap the book once the contracts settle.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- OIC: Gamma
- Cboe: Evaluating the Market Impact of SPX 0DTE Options
- FINRA: Options A to Z, Basics and the Greeks
- OIC: Open Interest, Why It Matters
How entries are sourced, calculated and updated: editorial methodology.