Part VIII · The whole market · Chapter 8A

Gamma exposure

From one book to the whole market

Where we are

Part VI followed one dealer through one trade: the delta hedge of Chapter 6C and the gamma of Chapter 6D that keeps undoing it. This chapter adds every dealer's gamma, across every strike and expiry, into one number called gamma exposure. It then turns that number into the trade dealers must make when the market moves, and shows that its sign rests on an assumption about who holds what.

What you need first

Gamma: the change in delta for a $1 move in the underlying. It is the same for a call and a put at one strike, and largest at the money and near expiry (Chapters 5C and 6D).
Delta hedging: the dealer trades the underlying to hold its book's delta at zero. A long-gamma book hedges against each move and a short-gamma book hedges with it (Chapters 6C and 6D).
The dealer holds the other side of each contract it trades, so its Greeks are the negatives of its customer's (Chapter 6B).
Dollar gamma per 1% move, about $46,000 for one at-the-money SPX contract at spot 6,000 (Chapter 6D).
Open interest and the contract multiplier (Chapters 5A and 5B).

The real market has thousands of strikes and dozens of expirations, holding, in the Dealer Mechanics Lab's phrase, hundreds of trillions of dollars of open interest. Adding up the dollar gamma of every dealer position, strike by strike and expiration by expiration, gives a single number. It is the gamma exposure index, or GEX, which tries to capture the total mechanical flow that dealers' hedging generates for each 1% move in the market.

This part of the book builds that number, maps it and tests it, in ten chapters:

This chapter constructs GEX and the hedge trade it implies.
Chapter 8B asks who holds what, since the sign of GEX rests on it, and how vendors estimate it.
Chapter 8C draws GEX strike by strike and expiry by expiry as a map, with Skylit's Heatseeker as the worked example.
Chapter 8D describes the two regimes the sign separates, and the mathematics of feedback.
Chapter 8E covers pinning at expiry, and Chapter 8F the flows from vanna and charm.
Chapter 8G reviews what studies have measured, effect by effect.
Chapter 8H studies the cases where the framework breaks, Volmageddon in 2018 and the March 2020 Great Liquidity Crisis among them. Chapter 8I turns those cases into a checklist for gamma squeezes.
Chapter 8J turns the whole part into a workflow for reading a map without being fooled by it.

The numbers this part cites come from academic research, peer-reviewed papers and working papers labeled as such, and from exchange and regulator data. Where a vendor's product or a bank desk's estimate is the subject, its own statements appear too, labeled as its claims. None come from social-media commentary.

In plain terms

Each dealer's hedge is small and mechanical. When the market moves 1%, a dealer's delta changes by its dollar gamma, and the dealer trades that amount back to stay flat. GEX adds all those trades together, each with a sign for its direction. A positive total means dealers as a group sell into rallies and buy into falls, which damps moves. A negative total means they buy rallies and sell falls, which pushes moves further. The catch is the sign: nobody publishes which side of each option the dealers hold, so every GEX number assumes it.

1 · One line of the chain, in dollars

Chapter 6D measured a position's gamma in the unit dealers use: dollars of hedging per 1% move. Call one strike, one expiry and one type (call or put) a line of the option chain, and label the lines $i = 1, 2, 3, \dots$ . Each line contributes

\Gamma_{\$,i} = s_i\,\Gamma_i\,S^2 M N_i \times 0.01

(8A.1)

where the symbols are:

symbol	meaning
$\Gamma_i$	the Black-Scholes gamma per unit of the underlying for that line (Chapter 5C)
$S$	the spot price of the underlying, the same on every line
$M$	the contract multiplier, 100 for SPX and SPY
$N_i$	the line's open interest, in contracts
0.01	the factor that converts "per $1 of spot" into "per 1% move"
$s_i$	+1 if dealers are assumed long the line, −1 if they are assumed short it

Data supply every symbol except the sign $s_i$ . Gamma itself is never negative, so the sign is the only part of the formula that says which way the line's hedge trades. It has to be assumed, and this chapter and the next are largely about it.

Why the formula has S squared

Step 1: the move. A 1% move in the underlying is $\Delta S = 0.01\,S$ .

Step 2: one option's delta. Gamma is the change in delta per $1 of spot, so each option's delta changes by $\Gamma_i \times 0.01\,S$ units of the underlying.

Step 3: the whole line. Each contract covers $M$ units and the line has $N_i$ contracts, so the line's delta changes by $0.01\,\Gamma_i S M N_i$ units.

Step 4: into dollars. Each unit is worth $S$ dollars, so that change is worth $0.01\,\Gamma_i S^2 M N_i$ dollars. One $S$ comes from the size of the move and the other from the price of what is traded.

Step 5: the dealer's side. A dealer who is long the line gains that delta on a rise. A dealer who is short it loses it. That difference is the sign $s_i$ . To stay flat, the dealer trades the opposite amount in the underlying.

Worked example: One at-the-money SPX contract

Step 1: the inputs. Take SPX at $S = 6{,}000$ and an at-the-money call with 30 days to expiry (DTE) at 18% implied volatility (IV). Its gamma, rounded, is $\Gamma = 0.0013$ per index point (Chapter 6D).

Step 2: the dollar gamma. By (8A.1) with one contract, $0.0013 \times 6{,}000^2 \times 100 \times 0.01 = \$46{,}800$ per 1% move. Chapter 6D's "about $46,000" is the same quantity before gamma is rounded.

Step 3: the hedge. A dealer short 1,000 of these contracts has $s_i = -1$ and a line total of −$46.8 million. A 1% rally leaves the dealer short about $46.8 million of extra delta, so the dealer buys that much SPX exposure to get back to flat.

2 · Adding up the market

Summing (8A.1) over every line of every expiry gives the market's total:

\text{GEX} = \sum_i \Gamma_{\$,i}

(8A.2)

GEX is measured in dollars per 1% move, and the Dealer Mechanics Lab writes it as $G_\$$ . This book calls it GEX and keeps the letter $G$ for the "destabilizing gamma" of Chapter 8D, which has the opposite sign.

The hedge flow

When spot moves, every dealer's delta moves with it, and each dealer re-hedges. Their combined trade in the underlying is the hedge flow. By (8A.2), a 1% move changes the dealers' combined delta by GEX dollars. A move of $p$ percent changes it by GEX times $p$ . To get back to flat they trade the opposite amount. Writing the move in percent as $p = (\Delta S/S)/0.01$ , the hedge flow in dollars is approximately

\Delta H \approx -\,\text{GEX} \times \frac{\Delta S / S}{0.01}

(8A.3)

The fraction divided by 0.01 is the move in percent: a 1% move multiplies GEX by 1, and a 0.5% move by 0.5. A positive $\Delta H$ is buying and a negative one is selling.

GEX > 0: the hedge trades against the move (contra-trend), which is stabilizing.
GEX < 0: the hedge trades with the move (pro-trend), which is destabilizing.

Desks often size such a flow in E-mini S&P 500 futures (ES), each contract worth $50 times the index (Chapter 2A). The number of contracts is

n_{\text{ES}} = \frac{\Delta H}{50\,S}

(8A.4)

Worked example: From a GEX number to a trade

Step 1: the reading. Suppose GEX is +$3 billion per 1% move, with SPX at 6,000.

Step 2: a 1% rally. By (8A.3), $\Delta H \approx -3 \times 1 = -\$3$ billion: dealers sell $3 billion of index exposure. One ES contract is $50 \times 6{,}000 = \$300{,}000$ , so by (8A.4) the sale is $3{,}000{,}000{,}000/300{,}000 = 10{,}000$ contracts.

Step 3: a 0.5% fall. $\Delta H \approx -3 \times (-0.5) = +\$1.5$ billion, so dealers buy 5,000 contracts into the fall.

Step 4: the other sign. At GEX of −$3 billion every trade reverses. The same rally meets $3 billion of buying and the same fall $1.5 billion of selling, each joining the move.

(8A.3) is a first-order approximation, and three assumptions sit inside it. Every dealer delta-hedges its whole book, at the Black-Scholes delta, as the price moves. The move is small enough that gamma barely changes; for a large one, reprice every line at the new spot instead (Chapter 5C). And the flow is gross: it counts what dealers must trade, not how much of it other traders absorb or add to. Chapter 8B shows where these assumptions break, and Chapter 8D how far a flow of a given size moves the price.

The figure draws (8A.3) for one value of GEX. One slider sets GEX in billions of dollars per 1% move, from −10 to +10 and starting at +3. A second sets the index move, from −3% to +3% and starting at +1%. A third sets spot, from 4,000 to 7,000, which changes only the conversion into ES contracts. The line is the trade at every move for the chosen GEX. The arrow is the trade at the chosen move, green when it opposes the move and rose when it joins it. Drag GEX slowly through zero.

GEX per 1% +$3.0B

index move +1.0%

spot 6,000

trade ΔH = −$3.00B

E-mini: sell 10,000 contracts

one E-mini = $300,000

Stabilizing. Dealers sell $3.00B into a 1.0% rally, against the move.

One sign decides which way the dealers trade. The line is the dealers' hedge trade, ΔH ≈ −GEX × (ΔS/S)/0.01, at every index move from −3% to +3%, for the GEX the slider sets in billions of dollars per 1% move. The arrow is the trade at the chosen move, green when it opposes the move and rose when it joins it. Past $10 billion it runs off the chart. The readouts give the same trade in E-mini S&P 500 futures, each contract $50 times the index at the chosen spot. Drag GEX through zero: the line leaves the green quadrants for the rose ones, and the same rally meets a purchase instead of a sale.

The figure opens on Step 2 of the worked example: a trade of −$3.00B and "E-mini: sell 10,000 contracts", with the verdict that the flow is stabilizing. As GEX passes through zero, the line leaves the green quadrants for the rose ones. At −3 the same 1% rally meets a $3.00 billion purchase, "with the move". At zero the readout says "No trade", because the dealers' hedge trades cancel whatever the move. Now set GEX to +7.5 and the move to −0.5%: dealers buy $3.75 billion, 12,500 contracts, the flow the stylized sum below arrives at.

(8A.3) is straight in the move, but the delta it approximates is not. The figure below reprices the option instead. Dealers are short 1,000 at-the-money SPX contracts, struck at 6,000 with spot at 6,000, and the index jumps at once by the move you set, from −5% to +5% and starting at +1%. The dashed line is (8A.3). The solid curve is the trade found by repricing the option's delta at the new spot. Both are counted in E-mini contracts, so no price conversion separates them. Two more sliders set the days to expiry, from 1 to 60 and starting at 30, and the implied volatility, starting at 18%.

index move +1.0%

days to expiry 30 days

implied vol 18%

formula: buy 154

repriced: buy 151

formula overstates by 2%

Good enough. At this move the formula is within 5% of repricing: buy 154 against buy 151 contracts. One contract carries $46,199 of dollar gamma per 1% move here, so the line totals $46.2 million.

Where the straight line stops being good enough. Dealers are short 1,000 at-the-money SPX contracts, struck at 6,000 with spot at 6,000, and the index jumps at once by the move on the horizontal axis. The dashed line is the hedge-flow formula, the gamma at 6,000 times the move. The solid curve is the exact trade, found by repricing the option's delta at the new spot. Both are drawn in E-mini S&P 500 futures, each on $50 times the index, so that no price conversion separates them. The rate is 4% and time counts calendar days. For small moves the two agree. For large ones the formula overstates the trade, most of all close to expiry, where gamma itself changes fastest.

At the start the formula says buy 154 contracts and repricing says 151, within 2%. The line's dollar gamma, $46.2 million per 1% move, is the worked example's $46.8 million before gamma is rounded. Drag the move to +3% and the formula overstates the trade by 10%: 462 contracts against 421. Now set the days to 1 and the move to +5%. The formula says 4,234 contracts and repricing 987: the straight line is more than four times too high. A day from expiry the option's delta can only rise from about 0.5 to 1, so the whole hedge is capped, while the straight line keeps climbing. Read GEX as the hedge for moves of a percent or so, and reprice for anything larger, above all near expiry.

3 · Who holds what: the sign chain

The sign of each line follows from a chain of four links. The customer's position fixes the dealer's, because the dealer holds the other side (Chapter 6B). The dealer's position fixes the sign of its gamma, because a long option has positive gamma and a short one negative. The gamma sign fixes the hedge: long gamma trades against the move, short gamma with it. The hedge fixes the effect on the market.

The first figure walks this chain one case at a time. Choose what the customer holds (long or short), the option (call or put), and which way spot moves (up or down). The first table follows the chain for your choice, and the second lists all four customer positions with yours marked. Start with a customer who is long a call and spot moving up, then switch the customer to short, then try a put.

customer is

option

spot moves

Derivation	This case
Customer	long call
Dealer (other side)	short call
Dealer gamma sign	short gamma
On spot up	dealer buys stock
Market impact	destabilizing

Customer	Dealer	Gamma	On up	On down	Impact
long call	short call	short gamma	buys stock	sells stock	destabilizing
short call	long call	long gamma	sells stock	buys stock	stabilizing
long put	short put	short gamma	buys stock	sells stock	destabilizing
short put	long put	long gamma	sells stock	buys stock	stabilizing

From the customer's position to the market's. Choose what the customer holds and which way spot moves, and follow it through: the dealer holds the other side, the dealer's gamma sign follows from that, and the gamma sign decides whether the hedge trades against the move or with it. The second table is all four base combinations, with the chosen one marked.

The figure opens on a customer long a call with spot moving up. The dealer is short the call and short gamma, and the readout says "dealer buys stock". That buying pushes the rally further, so the impact is destabilizing. Switch to a customer who sells a put and let spot move down. The dealer is long the put and long gamma, and buys stock into the fall, which cushions it. The option type turns out not to matter; only the side the dealer holds does. Customers who buy options, calls or puts, make hedging destabilizing, and customers who sell options make it stabilizing.

That corollary turns GEX into one question about customers. Near the money, where gamma is largest, are customers, on net, buyers or sellers of options, weighted by gamma? Net buyers leave dealers short gamma and GEX negative. Net sellers leave them long gamma and GEX positive.

Worked example: The chain with numbers

Step 1: one customer, one line. A customer buys 1,000 at-the-money SPX puts from a dealer, with SPX at 6,000, 30 days to expiry and gamma 0.0013. The dealer is short the puts, so $s_i = -1$ , and by (8A.1) the line carries −$46.8 million per 1% move. That is the size of the earlier example's calls, because a put's gamma equals a call's.

Step 2: a fall. If SPX falls 1%, (8A.3) has the dealer trade $-(-46.8) \times (-1) = -\$46.8$ million: it sells into the fall, pushing it further.

Step 3: a second trade. The same customer also sells the dealer 1,000 calls at the same strike and expiry. The dealer is now long the calls, +$46.8 million, and short the puts, −$46.8 million. The two lines cancel, and the dealer has nothing to re-hedge as spot moves. A long call and a short put at one strike make a synthetic long forward (Chapter 5F), which has no gamma.

So what counts is each line's net holder, weighted by its gamma, not how many contracts traded. A customer who both buys and sells options can leave the dealer's gamma where it was.

Filling in the sign

Public data show open interest, the number of contracts outstanding on each line, without showing who holds them. Every GEX model therefore fills in $s_i$ with a rule, a sign convention. Two conventions are widely quoted: the JPM-era convention counts every call +1 and every put −1, as if dealers were long calls and short puts. The 0DTE-era convention, named for same-day (0DTE) options, reverses both. Chapter 8B tells where each came from and what position data show, and for SPX the data fit neither. Here the two serve as assumptions to try on one book.

4 · A stylized sum

Chapter 6D's figure of about $46,000 per contract describes one contract. The claim that aggregate dealer GEX lives in the range of $20 billion to $100 billion per 1% move describes the sum. Walking one stylized sum end to end shows that the two orders of magnitude agree.

Worked example: Six lines of an SPX chain

Step 1: the setup. With SPX at 6,000, gamma follows a stylized profile that peaks at the money and decays symmetrically: about 0.0013 at the money, 0.0010 at 100 points away and 0.0006 at 200 points away. Open interest follows a typical put-heavy SPX profile, with puts below spot and calls above. The at-the-money strike is split 70/30, puts over calls.

Step 2: each line. The dollar gamma per contract comes from (8A.1) with one contract, and the line's total from multiplying by its open interest. The last column signs each line by the 0DTE-era convention, as the Dealer Mechanics Lab's example does: puts count positive and calls negative.

Strike	Type (assumed dominant)	OI (contracts)	$\Gamma$ per point	$ gamma per contract per 1%	Line total	Signed
5,800	puts	100,000	0.0006	$21.6k	$2.16B	+$2.16B
5,900	puts	200,000	0.0010	$36.0k	$7.20B	+$7.20B
6,000	puts	280,000	0.0013	$46.8k	$13.10B	+$13.10B
6,000	calls	120,000	0.0013	$46.8k	$5.62B	−$5.62B
6,100	calls	200,000	0.0010	$36.0k	$7.20B	−$7.20B
6,200	calls	100,000	0.0006	$21.6k	$2.16B	−$2.16B

Step 3: the sum. The puts give $2.16 + 7.20 + 13.10 = 22.46$ billion and the calls $5.62 + 7.20 + 2.16 = 14.98$ billion. The total is $22.46 - 14.98 \approx +\$7.5$ billion per 1% move.

Step 4: the flow. By (8A.3), a 1% rally has dealers selling about $7.5 billion of SPX exposure, 25,000 ES contracts. A 0.5% fall has them buying about $3.75 billion.

Step 5: the other convention. Under the JPM-era convention every sign flips, so the same open interest gives about −$7.5 billion. Dealers would then buy $7.5 billion into a 1% rally.

The first of three things in the example worth a second look is the sign. Nothing in the open interest changed between Step 3 and Step 5, only the assumption, and the verdict went from damping to amplifying.

The second is gross against net. The six lines carry $22.46 + 14.98 = 37.44$ billion of dollar gamma in all, yet they net to 7.5 billion, a fifth of the gross. A net that small is fragile. Get the sign of the puts alone wrong and the total becomes $-22.46 - 14.98 = -37.44$ billion, a swing of twice the puts' 22.46 billion.

Familiar ground

Net GEX behaves like a fluid balance chart. Intake and output are each large, and the net that guides treatment is their small difference. Chart one large output as intake and the net swings by twice that volume, enough to turn a deficit into an apparent surplus. A GEX total is also the net of large signed flows. There the sign of each flow is assumed rather than charted, so the same care applies twice over.

The third is the inputs. The Dealer Mechanics Lab calls the gamma profile stylized, and it is narrower than Black-Scholes gives. At 18% and 30 days, Black-Scholes gamma is about 0.00128 at the money, 0.00118 and 0.00125 at 100 points below and above, and 0.00098 and 0.00111 at 200 points. The Lab also says that more put than call open interest is the empirical norm because SPX skew is steep (Chapters 5E and 5G). The demand-based view of Chapter 8B reads the causation the other way: heavy end-user demand for index puts is what makes the skew steep.

5 · How big is big: scale in context

The toy has six lines, while the real listed SPX book has hundreds of strikes across several expirations. Its dollar gamma is also concentrated more sharply at short-dated at-the-money strikes than this snapshot shows. The Dealer Mechanics Lab scales the toy's total by a factor of 3 to 15, which it says the ratio of a real strip to the toy supports. That lands roughly in the range of $20 billion to $100 billion. The per-contract claim and the aggregate claim are then the same claim, summed at different grains.

Numbers that large need a yardstick. Cboe's research note "Much Ado About 0DTEs" (Mandy Xu, 2023) put the daily liquidity of S&P 500 futures at about $400 billion. It also measured something the Lab's range does not: the net gamma of market makers' same-day positions. Cboe rebuilt it from its own trade records, which flag each trade as a customer's or a market maker's.

Worked example: A GEX number against a day's trading

Step 1: the low end of the Lab's range. At $20 billion per 1%, a 1% rally asks dealers to sell $20 billion. By (8A.4) that is $20{,}000{,}000{,}000/300{,}000 \approx 66{,}700$ ES contracts at SPX 6,000, and $20/400 = 5\%$ of a day's futures liquidity.

Step 2: the high end. At $100 billion, the same rally asks for about 333,000 contracts, 25% of a day's futures liquidity.

Step 3: the measured same-day book. Cboe's 2023 note found market makers' net 0DTE gamma ranging from about $170 million to $670 million through the day. It put the resulting hedging flows at 0.04% to 0.17% of the daily S&P futures liquidity.

The Lab's range is 30 to almost 600 times Cboe's, and the two numbers measure different things. The Lab's range is a total over every expiry, with the sign assumed, and it counts the gross trade that hedging would require. Cboe's is a net position of market makers, measured rather than assumed, in same-day options only. Cboe's 2025 update, "0DTEs Decoded" (Xu, 2025), gave the reason it stays small: customer 0DTE activity "continues to be extremely balanced". It put net market-maker 0DTE hedging at "at best, just 0.2% of the SPX daily liquidity".

That figure concerns 0DTE market-maker hedging alone. Reading it as the size of all dealer hedging, or of the hedging around levels built from longer-dated open interest, is an inference the note does not make. The Edge Book cites it against trading GEX levels (Chapters 1G and 10H), and Chapter 8C returns to that argument.

Bank desks publish estimates of their own. A client note by Nomura's cross-asset strategist in March 2020 is known only as SpotGamma quoted it. It said that "the flows from option gamma hedging can account for 10-15% of total daily volumes on index futures". That is one desk's estimate, not a measurement, and its method is not public.

Dealers are also not the only traders whose flow follows the move. Leveraged ETFs and inverse ETFs rebalance with the day's move near the close (Chapter 6C). Tuzun (2013), a Federal Reserve working paper, estimated that a 1% rise in broad stock indexes induced these funds to trade the equivalent of $1.04 billion of stock, at the fund sizes of its sample. The trade always goes in the direction of the move. That flow has the same unit as GEX and a fixed sign. So dealer GEX is one term in the market's net response to a move, not the whole of it (Chapters 8D and 8H).

How far any of these flows moves the price depends on how deep the market is at that moment and on who takes the other side. That is the feedback coefficient of Chapter 8D.

In practice

When a vendor posts a GEX number, turn it into a trade before you think about it. Multiply by the move you care about and flip the sign, as (8A.3) does, then divide by $50 times the index for ES contracts. Set the result against a day's futures liquidity, about $400 billion in Cboe's 2023 note. Check the unit first: a number quoted per index point converts to one per 1% move by multiplying by one hundredth of the index (Chapter 8B lists the units in use). Your own options are a rounding error in these sums. The number matters to you as context for the trades you size, not as a trade of its own.

When it fails

The hedge flow fails when its assumptions fail. The sign can be wrong, since it is assumed (Chapter 8B). Dealers may trade options back out instead of hedging them, so open-interest gamma can overstate the flow (Chapter 8B). A large move changes gamma along the way, so the straight line misstates the trade. And open interest is counted once a day, so any intraday GEX is partly an estimate.

Decision rule

Before a GEX number enters a decision:

Convert it. Find its unit, turn it into a trade for the move you are sizing against with (8A.3), and set that trade against a day's futures liquidity.
Read the sign as an assumption. Until you know the vendor's sign convention and have checked it against Chapter 8B, treat the sign as unknown.
Use it as context, never as a trade. Do not size from the magnitude, which carries every limit of Chapter 8B. The Edge Book uses only the sign, at low confidence, to trim or keep the size of other trades (Chapter 10H). The Dealer Mechanics Lab reads the sign as the market's regime (Chapter 8D).

Common mistake: reading GEX as a forecast

GEX is positioning, not outcome. It tells you what dealers would trade if the market moved. It does not tell you whether the market moves, or which way. A large positive GEX says that a move would meet selling on the way up and buying on the way down. It does not say that the market stays still.

Common mistake: treating the flow as the price move

(8A.3) gives dollars traded, not index points moved. How far $7.5 billion of selling moves the index depends on the market's depth at that moment and on who takes the other side (Chapter 8D). The same GEX can mean a barely visible flow on a deep day and a real push on a thin one.

What to carry forward

One line's dollar gamma per 1% move is $s_i\,\Gamma_i S^2 M N_i \times 0.01$ , and GEX sums it over every line. Only the sign $s_i$ is not in the data.
The dealers' hedge flow is about −GEX per 1% move. Positive GEX trades against moves and damps them; negative GEX trades with them and amplifies them.
The sign chain runs customer, dealer, gamma, hedge, market. Customers who buy options make hedging destabilizing, and customers who sell them make it stabilizing.
The same open interest gives +$7.5 billion or −$7.5 billion in the stylized sum, depending only on the convention, and its net is a fifth of its gross.
Published sizes run from the Lab's $20 billion to $100 billion per 1% (gross, every expiry, sign assumed) down to Cboe's measured $170 million to $670 million (net, market makers, 0DTE only). A day's futures liquidity is about $400 billion.

6 · Check yourself

Question 1

A dealer is short 2,000 SPX calls with gamma 0.0010 per point, with SPX at 6,000. What is the line's dollar gamma per 1% move, and what does the dealer do if SPX falls 0.5%?

Answer

By (8A.1), $-1 \times 0.0010 \times 6{,}000^2 \times 100 \times 2{,}000 \times 0.01 = -\$72$ million per 1% move. By (8A.3), a fall of 0.5% gives $\Delta H \approx -(-72) \times (-0.5) = -36$ : the dealer sells about $36 million of SPX exposure into the fall. Short gamma trades with the move.

Question 2

When a customer sells a put to a dealer, what does the chain predict for the market when spot falls?

Answer

The dealer is long the put, so long gamma. On a fall the put's delta grows more negative, so the dealer becomes shorter in delta and buys the underlying to get back to flat. Buying into a fall is stabilizing.

Question 3

A vendor shows GEX of +$12 billion per 1% move with SPX at 6,000. What do dealers trade if the index falls 0.75%, in dollars and in ES contracts?

Answer

By (8A.3), $\Delta H \approx -12 \times (-0.75) = +\$9$ billion: dealers buy $9 billion into the fall. One ES contract is $50 \times 6{,}000 = \$300{,}000$ , so by (8A.4) the purchase is $9{,}000{,}000{,}000/300{,}000 = 30{,}000$ contracts.

Question 4

In the stylized sum the puts carry $22.46 billion of dollar gamma and the calls $14.98 billion, netting to about +$7.5 billion. What is the total if the puts' sign alone is wrong, and what does that say about small nets?

Answer

The total becomes $-22.46 - 14.98 = -\$37.44$ billion, a swing of 44.92 billion, twice the puts' dollar gamma. A net that is a small fraction of the gross can change sign, and by a large amount, when the assumed side of one large block is wrong.

Question 5

The Dealer Mechanics Lab puts aggregate dealer GEX at $20 billion to $100 billion per 1%, while Cboe measured market makers' net 0DTE gamma at $170 million to $670 million. Do the two contradict each other?

Answer

Not directly, because they measure different things. The Lab's range is a gross total over every expiry with an assumed sign. Cboe's is a measured net position of market makers in same-day options only. The comparison shows how much the answer depends on what is counted and on who is assumed to hold it, which is the subject of Chapter 8B.