Guide

Gamma hedging explained

Harbor Capital sold a block of one-week at-the-money calls on a large-cap tech name ahead of earnings, collecting $420,000 in premium. The desk delta-hedged at trade time — short 18,400 shares against the short-call book — and planned to leave the hedge static through expiration. By Thursday, the stock had whipsawed ±4% twice; the static hedge left the book net short delta on rallies and net long on dips, bleeding $63,000 in directional slippage before theta income could compensate. The PM asked whether gamma hedging — rebalancing the stock hedge as delta moved — would have preserved the vol-selling thesis. After modeling hedge P&L under realized vs implied paths, Harbor switched to dynamic delta bands and capped short-gamma notional at 15% of equity sleeve NAV.

Gamma is the rate of change of an option's delta with respect to the underlying price. It tells you how quickly your directional exposure shifts when the market moves — and therefore how often you must trade the stock (or futures) to stay neutral. This guide covers long vs short gamma economics, delta rebalancing mechanics, gamma scalping for market makers, the realized-vs-implied volatility trade, pin risk near expiration, the Harbor Capital earnings overlay refactor, a technique decision table vs static hedges and vol overlays, pitfalls, and a production checklist — building on options Greeks and volatility skew foundations.

Gamma in one picture

If delta is “shares equivalent” for an infinitesimal move, gamma is how fast that share count changes:

Gamma = d(Delta) / d(Spot)

Long call  → positive gamma (delta rises as spot rises)
Short call → negative gamma (delta becomes more negative as spot rises)

A portfolio's net gamma aggregates across strikes and expiries. Market makers who sell options to customers typically carry short gamma: they must buy stock on rallies and sell on dips to remain delta-neutral. Traders who buy straddles or wings ahead of events hold long gamma: they sell stock into strength and buy weakness, profiting when realized volatility exceeds what they paid in premium (see Black-Scholes for the model link between vol and fair value).

Where gamma concentrates

At-the-money (ATM) — gamma peaks when spot ≈ strike; OTM wings contribute little gamma until spot approaches them.
Near expiration — gamma explodes for ATM options in the final days; a 1% move can flip delta from 0.30 to 0.70.
Low implied vol environments — for a given move, higher nominal gamma per contract when vol is cheap (all else equal).

Ignoring gamma is tolerable for small, long-dated positions. It is dangerous for short-dated ATM books, earnings weeklies, and any size that moves P&L materially when delta drifts.

Delta hedging vs gamma hedging

Delta hedging sets stock/futures exposure to offset net option delta at a point in time. Gamma hedging is the ongoing process of rebalancing that hedge as spot moves so delta stays near target (usually zero for vol desks, or a strategic tilt for directional overlays).

Position	Spot rises	Static hedge error	Gamma hedge action
Short calls (short gamma)	Delta becomes more negative	Under-hedged — lose on rally	Buy more stock
Short calls (short gamma)	Spot falls	Over-hedged — lose on dip	Sell stock
Long straddle (long gamma)	Delta turns positive	Miss rally participation	Sell stock
Long straddle (long gamma)	Spot falls	Miss dip hedge benefit	Buy stock

The P&L from gamma hedging trades is often called gamma scalping P&L. For short gamma, you hope realized volatility is low enough that theta collected exceeds scalping losses. For long gamma, you need realized vol high enough that scalping gains exceed theta decay.

Rebalance triggers

Delta band — rebalance when |net delta| exceeds X shares or Y% of notional (e.g., ±500 shares or ±0.05 delta per contract).
Time schedule — every 15 minutes or at the open/close; simple but can over-trade in chop or under-hedge in gaps.
Spot move — rebalance after underlying moves Z% from last hedge point; ties frequency to gamma magnitude.
Vol regime — tighten bands when gamma per dollar rises (near expiry, ATM concentration).

Realized vs implied volatility economics

The central trade for gamma-aware desks:

Sell options (short gamma) — you collect implied vol via premium (theta). You pay for delta rebalancing when the stock moves (negative gamma scalping). Profitable if realized vol < implied vol you sold.
Buy options (long gamma) — you pay implied vol. You earn from rebalancing when moves are large (positive gamma scalping). Profitable if realized vol > implied vol you bought.

Rough intuition (ignoring skew, rates, and discrete hedging):

Short gamma P&L ≈ Theta income − 0.5 × Gamma × (realized move)²
Long gamma P&L  ≈ 0.5 × Gamma × (realized move)² − Theta decay

The squared term is why path matters: choppy, back-and-forth markets hurt short gamma (you buy high, sell low repeatedly) and help long gamma. Trending one-way moves can still hurt short gamma on the trend leg but help on mean reversion if it follows. Pair gamma views with skew-aware strike selection — selling rich OTM puts has different gamma/vega than ATM straddles.

Market-maker workflow

An equity options market maker quotes bids and offers, accumulates customer flow, and manages a book that is typically short options (short gamma, long theta):

Quote with edge over model fair value; adjust for inventory gamma and vega.
Fill updates net Greeks; auto-hedge engine fires if delta band breached.
Scalp stock/futures to re-center delta; log slippage vs mid.
Roll or spread risk across strikes/expiries to avoid single-name gamma cliffs.
End-of-day flatten toxic expiries or widen quotes into events.

Transaction costs and borrow fees eat gamma scalping edge. A desk that rebalances every tick in a low-vol grind can lose more in spreads than theta earns. Wider bands save costs but increase gap risk. Production systems log hedge efficiency: realized scalping P&L vs theoretical gamma P&L from a continuous model.

Pin risk at expiration

When spot settles near a large open-interest strike, dealers' gammas diverge as options flip between ITM and OTM. Pin risk is the uncertainty about final delta going into the close — you may over- or under-hedge into the auction. Mitigations: reduce gamma into the last session, spread expiries, use index futures for cleaner settlement, or accept small residual delta and hedge at the open next day.

Portfolio overlays beyond market making

Asset managers use gamma concepts even without running a quote book:

Covered calls — short call gamma means rally participation caps out; see our covered calls guide. Dynamic delta hedging of the short leg is rare for retail but institutional overwrite programs track gamma vs benchmark tracking error.
Collars and protective puts — long put gamma partially offsets short stock delta convexity on crashes; net gamma near flat until spot approaches put strike.
Variance swaps / vol swaps — pure realized-vs-implied exposure without discrete delta hedging on your side; dealer gamma sits on the other leg.
Earnings overlays — buying straddles into events is a long-gamma bet on realized move size vs implied; selling is the opposite.

Aggregate portfolio gamma with the same sign conventions as Greek aggregation: sum contract gammas × 100 × contracts, then stress spot ±1%, ±3% to see delta drift if you do nothing.

Harbor Capital earnings-week overlay refactor

Problem: short ATM weekly call overlay on a $180 stock, 12,000 contracts, static delta hedge at initiation, earnings Thursday after close. Stock ranged $172–$188 Mon–Wed with two 3% reversals; static hedge left −$63k scalping drag, theta only +$41k.

Implemented delta bands: rebalance when net delta exceeds ±800 shares (~0.04 Δ per contract × book).
Pre-earnings: cut 40% of ATM short gamma, replaced with slightly OTM calls (lower gamma concentration, less pin into strike).
Intraday hedge via SPY futures beta-adjusted hedge for partial cross-hedge when single-name borrow was tight.
Post-earnings: widen bands to ±1,200 shares for two sessions to reduce whip-saw costs while vol collapsed.
Capped total short-gamma notional at 15% NAV; breach triggers automatic quote pull / no new sales.

Backtest on prior four earnings cycles: dynamic hedging improved net vol-selling P&L by 22% after estimated transaction costs; largest gain in mean-reverting paths, modest cost in one-direction trend weeks.

Technique decision table

Approach	Gamma profile	Best when	Watch out for
Static delta hedge	Unmanaged gamma drift	Small, long-dated, low gamma	Short-dated ATM blows up
Tight-band gamma hedge	Short gamma, active scalp	Market making, short vol	Costs in low realized vol chop
Long straddle + scalp	Long gamma	Event vol underpriced	Theta bleed if move small
Wide-band / time hedge	Partial gamma control	Retail-sized books, lower turnover	Gap risk overnight
Futures cross-hedge	Basis-adjusted gamma	Borrow constraints on single name	Beta mismatch on idiosyncratic moves
Vol swap / variance swap	Delegated hedging	Pure vol view, scale	Counterparty, less strike control

Common pitfalls

Hedging gamma you do not understand — selling weeklies without rebalance infrastructure is a short-gamma bet, not “income.”
Over-tight bands — transaction costs exceed theta; log cost per rebalance.
Ignoring gaps — overnight earnings gaps jump over continuous hedge paths; size accordingly.
Pin into OI strikes — gamma sign flips near large open interest; reduce before expiry week.
Mixing vol and direction — a tilted delta target is fine if intentional; accidental drift from missed hedges is not.
Model vol vs realized — using stale implied vol in hedge sims misstates expected scalping P&L.
Skew-blind ATM sales — rich put skew may favor different structures than ATM strangles for the same vega.
No stress on gamma doubling — simulate spot ±5% with one day less time; gamma often doubles near expiry.

Production checklist

Compute net delta and gamma daily (or intraday for short-dated books).
Define rebalance bands and document who/what triggers hedges.
Estimate realized vs implied vol breakeven for the current book.
Log hedge trades with slippage vs mid; review weekly hedge efficiency.
Stress spot ±1%, ±3%, ±5% with unchanged hedge.
Flag expiries within 5 days where ATM gamma > X% of book gamma.
Plan pin-risk reduction into expiration Friday or monthly expiry.
Cap short-gamma notional as % of NAV or VaR limit.
Separate P&L attribution: theta, gamma scalp, vega, skew.
Reconcile broker Greeks vs internal model; investigate >5% gaps.

Key takeaways

Gamma tells you how fast delta drifts — static hedges decay as soon as spot moves.
Short gamma earns theta but pays on choppy paths; long gamma is the opposite bet on realized vol.
Rebalance bands balance hedge accuracy against transaction costs — there is no free continuous hedge.
ATM and near-expiry options concentrate gamma — pin risk is a gamma problem at settlement.
Harbor Capital cut earnings-week scalping drag with delta bands, OTM substitution, and a 15% short-gamma NAV cap.