Gamma: The Feedback Loop Hiding Inside Every Delta Hedge

Ride a bicycle down a hill that starts gentle and steepens toward the bottom, and the same single pedal stroke does something different depending on where you are. Near the top, on the gentle part, that stroke barely changes your speed. Near the bottom, on the steep part, the identical stroke changes your speed by far more. The hill hasn't asked you to pedal any harder — the slope underneath you has simply changed how much difference the same effort makes.

Delta was the gear ratio — how much an option's price moves for every rupee or dollar the stock moves. Gamma is the steepness of the hill underneath that ratio: how fast delta itself changes as the stock keeps moving. And in January 2021, gamma is the word that got attached to one of the most-watched stock moves in modern market history — GameStop rising from $19.95 to an intraday high of $483 in eleven trading days, a 2,321% move. The popular explanation was a "gamma squeeze." The regulator that actually investigated it came back far more careful than the headlines were.

What gamma actually is

An option's delta isn't fixed — it shifts as the stock price moves, climbing toward 1 as a call goes deeper in the money, sliding toward 0 as it goes further out. Gamma measures the speed of that shift: how many points of delta an option gains or loses for every rupee or dollar the underlying moves. If delta is how fast the option's price is moving relative to the stock, gamma is how fast that speed itself is changing — the acceleration sitting underneath the velocity.

Gamma isn't spread evenly across an option's life either, and it follows a pattern that will look familiar from theta: it's small for options that are deep in the money or deep out of it, and it peaks hardest for options sitting right at the strike price, with very little time left before expiry. That's the same stretch of an option's life where theta bites hardest too — which means the days an option is decaying fastest are also the days its delta is most unstable, liable to swing from 0.2 to 0.8 on a single sharp move in the stock.

Who has to react to it fastest

The same market makers who delta-hedge — the proprietary and algorithmic desks quoting Nifty and Bank Nifty options in India, firms like Citadel Securities and Susquehanna quoting on US exchanges — don't get to set their hedge once and leave it. A dealer who sells a call is short gamma: as the stock rises, the delta on that short call grows more negative, so the dealer has to buy more of the underlying just to stay flat. As the stock falls, the reverse happens, and the dealer has to sell. High gamma means that hedge has to be rebalanced constantly, in ever-larger size, the moment the stock gets close to the strike.

That's a cost dealers price in and structurally accept — but it means the size of their hedging trades isn't constant. It scales up automatically, without anyone deciding to trade more aggressively, exactly when an option is closest to the money and closest to expiry. Gamma is the reason a market maker's own defensive hedging can start looking, from the outside, like a trader chasing the market.

Why markets needed this

A dealer rebalancing a hedge in proportion to gamma is, most days, a stabilizing force — it's disciplined, mechanical, and small relative to the stock's total trading volume. The story changes when enough buying arrives on one side, in the same short-dated, near-the-money options, all at once.

GameStop in January 2021 is the case everyone reaches for. Retail traders coordinating on Reddit's WallStreetBets bought heavily into short-dated, out-of-the-money GameStop call options. The dealers who sold those calls had to buy GameStop stock to stay hedged — and as the stock price rose, gamma pushed the delta on those calls higher too, forcing dealers to buy still more stock, into a price that was rising partly because of that buying. That feedback loop, buying begetting hedging begetting more buying, is the textbook definition of a gamma squeeze, and GameStop's eleven-day, 2,321% run is the example every finance classroom now uses to teach it.

Except the US Securities and Exchange Commission's own October 2021 staff report on the episode was far more careful than that classroom retelling. Investigating the options data directly, SEC staff found that individual investors were buying far more GameStop put options than calls through the back half of January — put purchases climbing from $58.5 million on January 21 to $2.4 billion by January 27 — the opposite of what a pure gamma-squeeze story requires. The report's conclusion: neither a short squeeze nor a gamma squeeze fully explained the sustained rise, and positive sentiment sustained through Reddit and mainstream coverage did more of the work than options-driven hedging alone. That finding didn't go unchallenged — a group of finance academics later published a rebuttal arguing the SEC's own methodology understated gamma's contribution once dealer hedging on both puts and calls is modeled properly, and the dispute between the regulator's staff report and that academic critique remains unresolved. Gamma squeezes are real, mechanically. Whether one, alone, explains GameStop is still being argued in finance journals years later.

India hasn't had its own GameStop. What it has had is a case where a sophisticated trading firm allegedly stopped reacting to gamma and started manufacturing it. Because gamma peaks for options sitting at the strike price with little time left, at-the-money options expiring that same day are the most price-sensitive contracts a trader can hold — routine enough that Nifty (the sole weekly index contract left on NSE since Bank Nifty's weekly options were discontinued in November 2024) has long shown a documented tendency to drift toward a "max pain" strike in an expiry's closing hours, a pattern Zerodha's own trader-education material, Varsity, describes and teaches retail traders to watch for.

In July 2025, SEBI's interim order accused the US quant trading firm Jane Street of turning that same sensitivity into a strategy on 18 separate Bank Nifty and Nifty expiry days. The order describes Jane Street aggressively buying Bank Nifty's component bank stocks and their futures through the morning session — on some days over 20% of the market-wide traded volume in stocks like Kotak Bank, SBI, and Axis Bank — lifting the index, while simultaneously building a large short position in short-dated, at-the-money Bank Nifty and Nifty options. In the afternoon, SEBI's order says, the firm sold down those same stock and futures positions, a reversal that dragged the index back toward where it started — converting that options position, sized to be maximally sensitive to exactly this kind of late-session move, into profit. SEBI impounded ₹4,843.57 crore (roughly $566 million) in what it called unlawful gains and barred Jane Street's Indian entities from the market; a modification order three weeks later lifted the trading ban under new conditions, but the impounded funds stayed frozen.

Same underlying sensitivity, opposite postures toward it: US dealers pulled into a feedback loop they didn't start, in a case regulators are still debating the size of — and, in India, a trading firm SEBI accuses of engineering that same expiry-day sensitivity on purpose, ₹4,843.57 crore at a time.

Why this matters for a Business Analyst

Think of a thermostat that gets touchier the closer the room gets to the target temperature

A thermostat holding a room at a steady 5 degrees away from target barely reacts — small, occasional adjustments. Get within half a degree of the target, and the same thermostat starts cycling the heater on and off constantly, correcting itself far more often for the same-sized nudge in temperature.

"The desk's net delta is +2,400" — the same aggregate number covered earlier in this series — tells a risk report reader how exposed a book is right now. It says nothing about how fast that exposure can change. A book that's delta-neutral this second but carrying large negative gamma, because it's short a pile of near-the-money options expiring this week, can swing to badly exposed within minutes on a sharp move — the thermostat suddenly cycling nonstop. A BA building or reviewing a risk report for an options desk has to make sure gamma gets its own line, separate from delta, especially in the days before expiry — because a snapshot that only shows "how exposed is this book right now" can't answer the question that actually matters before expiry: "how much faster could that exposure change than the report refreshes?"

Lighthouse Insight

Go back to the hill. The bicycle's speed is delta. How fast that speed changes as the slope steepens is gamma — and the steepest part of any hill is exactly where a rider has the least room left to correct course before running out of road.

That's true whether the road is eleven trading days of retail call-buying against dealers who had no choice but to keep buying back in January 2021, or a Bank Nifty expiry afternoon that SEBI says one trading firm learned to engineer on purpose, ₹4,843.57 crore at a time. Gamma doesn't create the hill. It just tells you exactly where the same push starts producing a very different result — and in both markets, that's precisely where regulators, dealers, and academics are still spending the most time looking.