Dealer Hedging and “Gamma Squeezes”

What a dealer is, and why it hedges

An options market maker quotes both sides of thousands of series, earns the spread, and does not want a view on direction. Every trade leaves it holding options it did not choose — whatever customers wanted to buy or sell — so it neutralises the exposure, usually by trading the underlying shares. That is **delta hedging** (O10): a dealer short 1,000 calls with a delta of 0.40 is short the equivalent of 40,000 shares, so it holds 40,000 shares long and stops caring which way the stock goes, for now. For now, because the hedge does not stay right. A call’s delta grows as the stock rises — the rate is its gamma — so the dealer short calls has to **buy more shares as the price rises and sell as it falls**. That is the meaning of being **short gamma**: the hedging trades in the direction of the move and adds to it. A dealer long options faces the opposite arithmetic. Its delta grows against it as the stock rises, so it **sells into rallies and buys into declines** — long gamma hedging leans against the move and damps it. So the whole question of whether hedging amplifies or calms a market reduces to a sign and a size. Are the dealers net short or net long gamma — in that stock, at those strikes, at that moment? And is the resulting flow large or small next to everything else that trades? Every claim in this lesson is a claim about one or both of those numbers, and most of the confusion comes from stating the mechanism and skipping the measurement. • Dealers short options are short gamma: hedging buys rallies and sells declines — it amplifies. • Dealers long options are long gamma: hedging sells rallies and buys declines — it damps. • The flow in shares: contracts × 100 × gamma × the dollar move. One dealer, 1,000 short calls, a $2 rise — Delta 0.40 → the hedge: Long 40,000 shares · Stock rises $2; delta is now 0.55: The hedge must be 55,000 shares · The dealer buys 15,000 shares — into the rise: Short gamma: hedging adds to the move ← · If the dealer were long those calls: It sells 15,000 shares into the rise — damping

How big is the flow? Shares against a day’s volume

The arithmetic is short — shares to trade = contracts × 100 × gamma × the move — and the number of shares is not the point. What decides whether hedging can move a price is the size of that flow against a normal day’s trading, and that is where most “gamma squeeze” claims succeed or fail. Take the two books in this lesson’s calculator. Dealers short 200,000 calls on a $400 mega-cap with a gamma of 0.01 must buy 800,000 shares on a 1% rise — a large order, and 1.6% of a 50-million-share day. Dealers short 50,000 calls on a $20 small-cap with a gamma of 0.08 buy only 80,000 shares on a 1% rise, but that is 2.7% of its 3-million-share day, and on a 10% move it is about a quarter of a normal session. The same mechanism is a rounding error in one stock and a real force in another. Gamma is also concentrated. Almost all of it sits in **short-dated, near-the-money** contracts; a far-out-of-the-money call bought months before expiry barely moves a dealer’s hedge, while a cheap weekly call just above the price can move it a lot. That is why the mechanism is most plausible where speculative buying piles into short-dated calls near the price of a stock with limited float and volume — and least plausible in a broad index on an ordinary day. And the flow is bounded. A dealer never needs more than 100 shares per contract it is short; once the calls are deep in the money, delta is close to one, the hedge is complete and the buying stops. A loop that can only add up to the delta of the open interest is a burst with an end, not a machine that runs forever — which is one reason squeezes, however violent, are short. • Flow = contracts × 100 × gamma × the dollar move. • Compare it with average daily volume, not with a headline count of calls. • Gamma lives in short-dated, near-the-money contracts. • The total is capped at 100 shares a contract — the loop ends when the calls are deep in the money. The same mechanism, two stocks (this lesson’s calculator) — Mega-cap, 1% rise: 800,000 shares — 1.6% of a day · Small-cap, 1% rise: 80,000 shares — 2.7% of a day · Small-cap, 10% rise, gamma held fixed: About 800,000 shares — 27% of a day ← · Small-cap, if dealers were long the calls: They sell 80,000 shares on a 1% rise

The sign nobody publishes

Here is the problem every gamma story runs into: public data does not say who is short. **Open interest** counts the contracts outstanding, not which side the dealers hold. **Volume** counts trades, not whether the customer bought or sold. A call traded may be a speculator buying from a dealer, which leaves the dealer short gamma, or a fund writing covered calls to a dealer, which leaves the dealer long gamma — and the tape looks identical. Commercial “gamma exposure” estimates fill the gap with assumptions — commonly that customers buy puts and sell calls on indexes, or buy calls on single stocks — and publish a number for dealer gamma. They can be a rough map, but they are models of the sign, not measurements of it, and a confident chart built on one carries every assumption inside it. A trader who sizes positions off a published dealer-gamma level should know that the number’s most important digit — plus or minus — is the one that was assumed. The evidence that hedging flows matter does exist, and it is careful about the sign. Ni, Pearson and Poteshman found that the closing prices of optionable stocks cluster at strike prices on expiration days — pinning — consistent with rebalancing by delta-hedgers who are net long options. Baltussen, Da, Lammers and Martens found that hedging demand from short-gamma positions helps explain why index returns late in the session tend to continue the direction of the earlier part. And as same-day options grew — 59% of SPX volume in 2025, by Cboe’s count — a 2024 study by Dim, Eraker and Vilkov found that higher open-interest gamma in those short-dated options went with lower, not higher, volatility within the day, and that surges in their volume did not amplify recent index moves. Every one of those effects is real and modest; none of them says that buying calls makes a stock go up. • Open interest: how many contracts exist — not who holds which side. • Volume: how many traded — not who bought. • Vendor gamma estimates: an assumption about the sign, presented as a number. • Documented effects: pinning at expiry, late-day index momentum, short-dated gamma damping intraday volatility. A chart of call volume next to a rising price shows that two things happened at once. It does not show which caused which, or which side the dealers were on.

Claims against evidence: the GameStop test

GameStop is the case everyone cites, and it is the best test available because a regulator later examined it with data the commentators never had. The SEC’s staff report of October 2021 found that individual customers’ options volume in GME rose from $58.5 million on January 21 to $563.4 million the next day and peaked at $2.4 billion on January 27 — but that the increase was **mostly put buying**, and that market makers were **buying calls rather than writing them**. Those observations are the opposite of the position a gamma squeeze needs, and the staff said plainly that it did not find evidence of one. It also found that buying by accounts with large short positions was a small fraction of overall buy volume, and concluded that positive sentiment, not buying-to-cover, sustained the weeks-long rise. Two cautions keep the conclusion honest. A committee of academics later argued that the staff’s gamma analysis was incomplete and could be extended to net every market maker’s hedges across both puts and calls, so the question is debated rather than closed. And the report’s own figures show how extreme the options market became: implied volatility on GME’s at-the-money contracts reached about nine times its typical 2020 range, which also means the calls were extraordinarily expensive — hardly the cheap lever the viral account described. What changed is the burden of proof. The popular story had stated as fact a mechanism its own evidence never showed. Four questions turn a viral claim into a testable one. **Who is short** the options — dealers or customers? **How large** is the hedge flow against normal daily volume? Does the **timing** fit — did the hedging come before the price moves it is said to cause? And **what does the position data show**, and who has it? The SEC had the fourth; most commentators had none of the four. The same questions apply to every later story about options flows moving a market, including the ones told about the index every day. • Who is short the options — dealers or customers? • How large is the hedge flow against normal daily volume? • Does the timing fit — hedging before the move it supposedly caused? • What does the position data show, and who has it? What the SEC’s staff found in GME, January 2021 — Customer options volume, January 21 → 27: $58.5 million → $2.4 billion · What drove the increase: Mostly put buying · Market makers in calls: Buying, not writing ← · Short covering: A small fraction of overall buying · Conclusion: No evidence of a gamma squeeze; sentiment sustained the rise

Sources

• GameStop, January 2021: options volume, market makers and a gamma squeezeSEC — Staff Report on Equity and Options Market Structure Conditions in Early 2021 (October 2021)
• Stock prices clustering at strikes on expiration datesNi, Pearson & Poteshman, “Stock Price Clustering on Option Expiration Dates” (Journal of Financial Economics, 2005)
• Hedging demand and late-day index momentumBaltussen, Da, Lammers & Martens, “Hedging Demand and Market Intraday Momentum” (Journal of Financial Economics, 2021)
• Short-dated options, dealer gamma and intraday volatilityDim, Eraker & Vilkov, “0DTEs: Trading, Gamma Risk and Volatility Propagation” (2024)
• SPX 0DTE share of SPX volume, 2025Cboe Global Markets, full-year 2025 volume report