Part IX · Volatility in practice · Chapter 9B

Same-day options

0DTE and the singularity at the strike

Where we are

Chapter 9A built the VIX and its term structure, down to the one-day VIX1D. This chapter goes to the shortest horizon of all: options that expire on the day they trade. It shows why their gamma piles up at the strike, what the evidence says about whether they have destabilized the market, and why the end of the day now runs on a clock.

What you need first

Gamma, $\Gamma = \varphi(d_1)/(S\sigma\sqrt{T})$ with no dividends, largest at the money (Chapter 5C), and the dealer's chase of delta that it forces (Chapter 6D).
Charm and speed, which grow as expiry nears (Chapter 5D).
Gamma exposure, whose sign rests on an assumption about who holds what (Chapter 8B), and the two regimes that sign separates (Chapter 8D).
The closing auction and market-on-close orders (Chapter 2C).

1 · The rise of same-day options

The most consequential shift in modern equity microstructure is the rise of zero-days-to-expiration options, or 0DTE options, which expire on the day they trade. From under 5% of SPX volume in 2016, 0DTE reached 62.4% of all SPX volume in August 2025 and 60% in September 2025. Its monthly averages ran between 56% and 62% across all of 2025. Average daily 0DTE volume hit 2.4 million contracts in August 2025. Total SPX options volume hit a record 4.26 million contracts a day in September 2025.

Industry-wide, 0DTE was approximately 24% of all US listed options volume by late 2024. The Dealer Mechanics Lab describes it as on track to grow further. It calls this the largest single shift in options market structure since the launch of SPX weekly options in 2005.

2 · Why expiry concentrates gamma

The mechanical reason 0DTE matters is the gamma formula of Chapter 6D: gamma grows as $1/\sqrt{T}$ . At the money $d_1$ is close to zero, so $\varphi(d_1)$ is close to its peak of 0.399, and at-the-money gamma is about $0.399/(S\sigma\sqrt{T})$ . With spot and volatility held fixed, the ratio of at-the-money gamma at two times to expiry is therefore

\frac{\Gamma(T_1)}{\Gamma(T_2)} \approx \sqrt{\frac{T_2}{T_1}}

(9B.1)

Worked example: Four hours against thirty days

Step 1: put both times in hours. Thirty days is $30 \times 24 = 720$ hours. Only the ratio of the two times enters (9B.1), so the unit does not matter.

Step 2: take the square root. At-the-money gamma four hours before expiry is $\sqrt{720/4} = \sqrt{180} = 13.4$ times its 30-day value. Half an hour before expiry it is $\sqrt{1{,}440} = 37.9$ times.

Computing $T$ in years for consistency, the Dealer Mechanics Lab tabulates the divergence:

Days to expiry	$T$ (years)	$\sqrt{T}$	Gamma ratio against 30 days
30 days	0.0822	0.2867	1.0× (baseline)
7 days	0.0192	0.1385	2.07×
1 day	0.00274	0.0523	5.48×
4 hours	$4.57 \times 10^{-4}$	0.0214	13.4×
30 minutes	$5.71 \times 10^{-5}$	0.00756	37.9×
5 minutes	$9.51 \times 10^{-6}$	0.00308	93.0×

These ratios apply to at-the-money gamma. Away from the strike, time works the other way: as $T$ shrinks, gamma compresses into the at-the-money strike and out-of-the-money gamma collapses, which is the negative color of Chapter 5D.

This concentration produces the strange 0DTE consequence. When a dealer is short a slightly out-of-the-money 0DTE call and spot ticks above the strike, delta jumps from near zero to near one almost discontinuously. The dealer must buy a large block of stock at that strike.

Worked example: One strike, one hour before the close

Step 1: the call's delta across the strike. Take a 0DTE call struck at 6,000 with one hour left, implied volatility at 15% and a zero rate, so $T = 1/8{,}760$ of a year. Spot's one-sigma move over that hour is $6{,}000 \times 0.15 \times \sqrt{1/8{,}760} = 9.6$ points. With spot at 5,988 the delta is 0.106, and with spot at 6,012 it is 0.894.

Step 2: the dealer's buying. A dealer short 1,000 of these calls must hedge $(0.894 - 0.106) \times 100 \times 1{,}000 = 78{,}800$ more share-equivalents as spot crosses those 24 points, a move of 0.4%. The same call with 30 days left would need only about 3,700.

Step 3: the ratio. The hour-before-close hedge is about 21 times the 30-day one across this range, close to the $\sqrt{720} = 26.8$ of (9B.1) at the strike itself.

When many dealers face this near the same level, the Dealer Mechanics Lab calls the result the "magnet": price snapping to a strike where hedging flow concentrates. Which way that flow pushes depends on the sign of the dealers' gamma. Dealers short the calls buy as spot rises through the strike, which presses the move on. Dealers long options at the strike sell above it and buy below it, which holds price near it, the pinning of Chapter 9C.

The figure below draws gamma for a $100-strike option with an implied volatility of 18%, across spot from $92 to $108. Faint lines are fixed references at 30, 7 and 1 days to expiry. The bold curve is the days to expiry on the slider, which runs on a logarithmic scale from 0.05 days, about an hour, to 90 days, starting at 30. The vertical scale follows the bold curve's peak, so the references flatten as it grows. Readouts give the at-the-money gamma, its ratio to the 30-day baseline, and the $1/\sqrt{T}$ expectation for that ratio.

Drag the slider down to about 0.17 days, which the readout shows as 4.0 hours, and compare the two ratios. Then press auto-shrink, which runs the clock down to about an hour and starts again from 90 days, or reset to return to 30.

DTE (log scale) 30.0 days

ATM gamma = 0.0770

vs 30-DTE baseline = 1.0×

1/√T expectation = 1.0×

Gamma piles into the strike as expiry nears. The gamma of a $100-strike option (σ = 18%) across spot from $92 to $108. The faint lines are fixed references at 30, 7 and 1 days to expiry; the bold curve is the DTE on the slider, and the vertical scale follows its peak, so the references flatten as it grows. Drag DTE down, or press auto-shrink to run the clock down to about an hour (and round again from 90 days): at 4 hours the at-the-money peak is about 13 times the 30-day one, the 1/√T divergence of the table above.

At 30 days the at-the-money gamma reads 0.0770. At 4 hours the peak is about 13 times the 30-day one, 13.5 on the readout against an expectation of 13.4. The curve has become a spike a few dollars wide. At about an hour the ratio reads 24.6 against an expectation of 24.5. The reference curves shrink to a flat line near zero, because the vertical scale follows the peak.

3 · Did 0DTE break the market?

Given the gamma maths above, a reasonable concern is whether 0DTE has destabilized markets. The Dealer Mechanics Lab answers no: on average it has reduced realized volatility. It cites Cboe's own data, Dim, Eraker and Vilkov (2023), and the 2025 successor paper of Adams and colleagues. The studies that measure dealers' positions in SPX support that answer. One study that measures 0DTE trading volume instead finds the opposite, so the evidence is split rather than settled. The reasoning on each side is subtle and worth unpacking.

How big the hedging flow is

Cboe's analysis, "Much Ado About 0DTEs" by Mandy Xu (September 2023), tracked market makers' net gamma in SPX 0DTE options in half-hour steps through the day. On average it ran from about $170 million to $670 million as the day went on. At 3:30 PM the median was about +$173 million per percentage point, within what Cboe calls a typical range of −$1.1 billion to +$2.4 billion. "Per percentage point" means that for each 1% move in SPX, hedging at that median trades about $173 million of the index. For context, S&P futures trade about $400 billion in daily liquidity.

Worked example: The flow as a share of the market

Step 1: Cboe's own range. The average net gamma, $170 million to $670 million, set against $400 billion of daily futures liquidity, gives $170/400{,}000 \approx 0.04\%$ to $670/400{,}000 \approx 0.17\%$ . These are the figures Cboe reports.

Step 2: the median at 3:30 PM. A 1% move asks for $173 million of hedging, which is $173/400{,}000 = 0.043\%$ .

Step 3: the top of the typical range. Even at +$2.4 billion per point, a 1% move asks for $2{,}400/400{,}000 = 0.6\%$ of a day's futures liquidity.

The Dealer Mechanics Lab reads Cboe's 0.04% to 0.17% as meaningful but not market-moving on a typical day. It quotes that range as the flow "at the median". Cboe's range in fact describes the average through the day. The 3:30 PM median, 0.043%, sits near its low end. The Edge Book cites a 2025 Cboe estimate of the same order. Xu's "0DTEs Decoded" (May 2, 2025) puts net market-maker 0DTE gamma hedging at "at best, just 0.2% of the SPX daily liquidity". The Edge Book draws from that a more skeptical conclusion about trading on dealer gamma (Chapters 1G and 10H). Because both Cboe figures measure same-day hedging only, reading them against GEX levels built mostly from longer-dated open interest extends the measurement.

Familiar ground

A 0DTE contract's gamma is like a large hazard ratio on a rare event. The relative effect is enormous: 13 times the 30-day gamma four hours out. Yet the absolute flow it produces is a small fraction of the market. A treatment that triples the risk of an event with a 0.1% baseline adds 0.2 percentage points of absolute risk. You judge its clinical weight by that absolute number, and 0DTE hedging by its share of the day's liquidity.

The academic evidence

Dim, Eraker and Vilkov (2023), a working paper first posted in November 2023, which the Dealer Mechanics Lab calls the academic gold standard on this topic, found:

"... Market Makers' inventory, as measured by the net gamma of their positions, is on average positive and negatively related to future intraday volatility."

Dim, Eraker and Vilkov (2023)

The authors add that their evidence is "consistent with delta-hedging but inconsistent with information-based trading." The Dealer Mechanics Lab's translation runs as follows. Most 0DTE flow, in its account, is retail and small institutions selling premium, through credit spreads, iron condors and cash-secured puts. The dealers buy it, so they are long gamma in aggregate in 0DTE. Their hedging, which sells rallies and buys dips, is therefore stabilizing. The Lab calls that the opposite sign from the original SqueezeMetrics convention (Chapter 8B). It takes the result to explain why intraday volatility has compressed even as headline option volume has exploded.

That translation is the Lab's, not the paper's. Dim, Eraker and Vilkov infer market makers' inventory from end users' order flow. They do not attribute it to retail premium selling. The flow data point elsewhere:

Customers' buying and selling are about balanced. Amaya, Garcia-Ares, Pearson and Vasquez (2025) work from proprietary records of every SPX and SPXW trade from January 2020 to June 2023. On the average day in that sample, customers buying 0DTE options from market makers made up 14.95% of all SPX and SPXW volume. Customers selling to them made up 14.06%. Cboe calls customer 0DTE activity "very balanced".
The retail slice that can be identified was a net buyer. Beckmeyer, Branger and Gayda (2023) identify retail orders by their routing to Cboe's price-improvement auctions, from February 2021 to September 2023. Those investors bought more 0DTE options than they sold, which left market makers net short them.
The dealers' long gamma comes mostly from older positions. Adams, Fontaine and Ornthanalai (2024) find that market makers pass most same-day 0DTE orders straight through. The positions they keep come from customers' trades in longer-dated options, which become 0DTEs as they near expiry.

Position data also argue against a fixed sign for each option type. Across all SPX options from 2011 to 2023, dealers held a persistent net short position of about 19 million puts, mostly deep out of the money, with calls near zero (Terstegge 2025). That is the put side of the original SqueezeMetrics convention, not the long puts that the 0DTE-era convention assumes. Dealers can be long gamma near the money on most days while short those far puts, whose gamma grows in a sell-off. Read every sign as an assumption about who holds what.

Adams, Dim, Eraker, Fontaine, Ornthanalai and Vilkov (2025), posted December 3, 2025, extend this finding with a natural experiment and identify the mechanism more precisely. Cboe listed Tuesday SPXW options from April 18, 2022 and Thursday ones from May 11, 2022. The first of them expired on April 26 and May 19. Using those two steps, they show:

"The presence of 0DTEs dampens market volatility through a shift in market makers' hedging needs. Importantly, this shift occurs not due to trading 0DTEs on their expiration day but due to positions in longer-dated options accumulated earlier and becoming 0DTEs."

Adams, Dim, Eraker, Fontaine, Ornthanalai and Vilkov (2025)

This is critical. The dampening works through longer-dated positions becoming 0DTEs as time passes, not through trading on the expiration day. Once Tuesday and Thursday joined Monday, Wednesday and Friday, every weekday had an expiration. The structural existence of more 0DTE expirations changes the dynamics of dealer hedging across the whole life cycle of an option, not just on the day it expires.

Brogaard, Han and Won (2023), a working paper first posted in April 2023 and revised since, reach the opposite conclusion with a different design. They study 0DTE trading in index options from January 2011 to August 2023. As an instrument for that trading they use the staggered introduction of weekly index options, an instrumental-variables design rather than an event study. By their estimate, a one-standard-deviation rise in 0DTE trading raises volatility by 9.10% of its mean, or 15.91% of its standard deviation. The effect stays positive after they control for market makers' gamma hedging. They attribute it mainly to speculative retail investors.

Familiar ground

The two new expiration days arrived on two dates, 23 days apart, which makes them a stepped rollout of a single intervention. It is the logic of a stepped-wedge design, in which the same market is observed before and after each step. The second step gives a second chance to see the effect. The steps were not randomized, so anything else that changed around those dates is a candidate confounder. Brogaard, Han and Won's design is closer to Mendelian randomization: an instrument, the listing of weekly options, stands in for the exposure. It holds only if the listings moved volatility through 0DTE trading and nothing else. Two non-randomized designs, each with its own weak point, point opposite ways, so neither settles the question alone.

The Dealer Mechanics Lab describes an academic consensus, as of late 2025 and early 2026, that 0DTE has stabilized rather than destabilized SPX intraday markets on average. In its account, that consensus still allows episodic destabilization when dealer positioning flips negative. The studies are split rather than agreed. Those that measure market makers' SPX positions find damping on average: Dim, Eraker and Vilkov, and Adams and co-authors. Amaya, Garcia-Ares, Pearson and Vasquez (2025) bound the worst case, putting the most that market makers' 0DTE gamma can add at 3.3 percentage points of annualized daily volatility. Brogaard, Han and Won, measuring trading volume, find amplification. For single stocks, Ellahie, Kaplan, Potter and Saha (2025) find that listing weekly options raised volatility. The split follows the method (positions against volume) and the market (the index against single stocks).

4 · Quiet most days, sharp on event days

The Dealer Mechanics Lab adds that 0DTE can be episodically destabilizing: the right tail is real. The dangerous days are event days: the Federal Reserve's rate decisions (FOMC), consumer price releases (CPI) and the monthly jobs report (nonfarm payrolls, NFP). When net dealer 0DTE gamma flips short on such a day, the small notional combines with the enormous per-contract gamma. The result is concentrated flow that can amplify intraday moves. The character of the modern market is therefore "quiet most days, sharp on event days": punctuated equilibria, driven by which side of gamma dealers sit on at the moment.

The Lab's examples are the April 2025 "Liberation Day" tariff-related sell-off and the October 10, 2025 follow-through. The second of these, it says, set the single-day options volume record of 110 million contracts. It reads dealer gamma in 0DTE on those days as likely net short, because retail was buying directional protection rather than selling premium. The hedging flow, in its account, then amplified the directional move. The Lab gives no source for that reading, and none has been found. The only data found on retail behavior in the April episode are Cboe's: retail's share of SPX 0DTE volume fell to 47% during the spike, then rose back to about 60% as volatility abated. A share of volume says nothing about which way that retail flow traded.

5 · The intraday charm clock

Charm, the drift of delta with time, scales with $1/T$ (Chapter 5D). For a 0DTE option that factor builds aggressively through the day. Its delta decays smoothly through the morning, then accelerates dramatically after lunch. By 3:30 PM Eastern Time (ET), charm has typically delivered most of its mechanical flow.

Worked example: A call struck 0.2% above spot, from the open to the close

Take a 0DTE call struck at 6,012 with spot held at 6,000, implied volatility at 15% and a zero rate. The option expires at the 4:00 PM close, so at 9:30 it has 6.5 hours left.

Time (ET)	Hours left	Delta
9:30 AM	6.5	0.313
11:30 AM	4.5	0.279
1:30 PM	2.5	0.216
3:00 PM	1.0	0.106
3:30 PM	0.5	0.039

Step 1: the morning. From 9:30 to 11:30 the delta falls by 0.034, with spot unchanged.

Step 2: the afternoon. From 1:30 to 3:30 it falls by 0.177, more than five times the morning's pace. By 3:30 it has lost 0.274 of its 0.313, 88% of the day's decay.

Step 3: the dealer. A dealer long 1,000 of these calls, bought from a premium seller, opens with a short hedge of 31,300 share-equivalents. With spot never moving, charm alone makes it buy back 17,700 of them between 1:30 and 3:30.

This is one reason the last 30 minutes of the day have become even more mechanical in the 0DTE era. That window was already concentrated for end-of-day rebalancing, as Baltussen et al. (2021) documented (Chapter 6C). Three flows now arrive in the same 30 minutes:

Charm-driven dealer rebalancing in 0DTE options.
End-of-day delta rebalancing of longer-dated dealer positions.
Mechanical flow from passive funds in the closing auction.

The evidence for a mechanical close is narrower than that list suggests (Chapter 6C). Baltussen and co-authors documented late-day momentum in index and other futures, where they tie it to short-gamma hedging. Among individual stocks, Baltussen, Da and Soebhag (2024) find a reversal in the last 30 minutes instead: the day's losers bounce against its winners. They find that gamma hedging does not explain it.

For retail traders the implication is that the last 30 minutes are not a normal trading window. Strategies that work in the middle of the day may not work in the close. Strategies that explicitly target the close, such as market-on-close orders (MOC) into rebalancing flow, work differently from strategies that try to fade the close with mean reversion against mechanical flow.

6 · Who trades 0DTE

Cboe's late-2025 disclosures, through Mandy Xu's monthly volatility digest, show that retail trading makes up roughly 50% to 54% of total SPX 0DTE volume as of mid-2025. The retail share has grown structurally as Robinhood, in January 2025, and other retail brokers expanded access to index options. That share is Cboe's own estimate. Beckmeyer, Branger and Gayda's auction-based identification, a much narrower slice, puts retail at about 6% of 0DTE trading.

The Dealer Mechanics Lab holds that retail 0DTE flow is mostly premium selling, credit spreads and iron condors, not directional purchases. In its account, this is what keeps dealers net long gamma in 0DTE on most days. The data earlier in this chapter do not bear that out. Customers' buying and selling are about balanced. The identifiable retail slice was a net buyer. The dealers' long gamma comes mainly from longer-dated positions rolling into expiry. Cboe's 2025 note makes the general point: what matters for market makers' hedging is "the balance of the volume between buys vs. sells, not the notional size".

The Lab's warning still stands as a scenario. Suppose customer flow turned one-sided toward buying, for example during a sustained bull market with aggressive retail call buying. Dealers would then be net short gamma in 0DTE. The same product that damps moves on average could then amplify them. Nothing ensures that the balance holds. Chapter 8B's warning applies in full: every sign here is an assumption about who holds what.

In practice

If you sell 0DTE premium, you are short the gamma this chapter describes. An hour before the close, a 0.4% move across your short strike can swing its delta from 0.1 to 0.9, about 21 times what the same move does to a 30-day option. A defined-risk spread caps the loss, but not the speed at which you reach it. The Edge Book also counts 0DTE premium selling as one more short-volatility sleeve, which in a liquidity event moves with every other one (Chapter 10H).

If you trade the index rather than its options, the chapter still reaches your account twice. Event days can turn the usual damping into amplification. The last 30 minutes run on flows that have nothing to do with the news.

When it fails

The stabilizing result comes from studies of dealers' positions. A study of trading volume disputes it. Even taken as given, the result is an average over days. It says nothing about the event days in the right tail, when dealer 0DTE gamma can turn short. The Dealer Mechanics Lab believes it did in April and October 2025, but gives no source. The result also rests on the balance of customer buying and selling, which Cboe measures but which can change. Every public estimate of dealer gamma assumes who holds what (Chapter 8B), so a vendor's reading can have the wrong sign on exactly the day it matters.

Decision rule

On FOMC, CPI and NFP days, assume dealer 0DTE gamma may be short. Do not sell 0DTE premium into the release at your usual size.
Size a short 0DTE option for its afternoon gamma, not its morning delta: the size you could hold through a 0.4% move across the strike in the last hour.
Treat the last 30 minutes as a separate window. Decide in advance whether a trade there goes with the closing flow, as an MOC order does, or against it. Do not carry a midday strategy into it by default.

Common mistake: reading 0DTE volume as dealer risk

Volume says how much traded, not who holds what. Half of 0DTE volume being retail says nothing on its own about the sign of dealer gamma, which turns on the balance of buying and selling. A day of heavy 0DTE volume becomes dangerous when the flow turns one-sided, not because it is heavy.

What to carry forward

At-the-money gamma grows as $1/\sqrt{T}$ : 13.4 times its 30-day value four hours before expiry, 37.9 times at 30 minutes and 93 times at 5 minutes.
Near expiry a dealer's hedge jumps from almost nothing to almost everything as spot crosses the strike.
Studies of dealers' SPX positions find that 0DTE has reduced realized volatility on average, through longer-dated positions becoming 0DTEs (Adams et al. 2025) rather than retail premium selling. A study of 0DTE trading volume finds the opposite, so the question is open.
Event days are the exception: "quiet most days, sharp on event days".
Charm delivers most of a 0DTE option's delta decay by 3:30 PM, which makes the last 30 minutes a mechanical window.

7 · Check yourself

Question 1

By what factor does at-the-money gamma grow between 30 days and one hour before expiry, with spot and volatility unchanged?

Answer

By (9B.1) it grows by $\sqrt{720/1} = 26.8$ , since 30 days is 720 hours. The figure's readout at about an hour, 0.05 days, gives about 24.5, the ratio for 1.2 hours.

Question 2

With market makers' net 0DTE gamma at Cboe's 3:30 PM median, SPX moves 2%. How much hedging does that ask for, as a share of futures liquidity?

Answer

About $2 \times \$173$ million, or $346 million, which is $346/400{,}000 = 0.087\%$ of $400 billion. That is meaningful but not market-moving, in the Dealer Mechanics Lab's phrase, and it covers same-day hedging only.

Question 3

What happened to SPXW options in the spring of 2022, and what did Adams et al. (2025) find about where the dampening comes from?

Answer

Cboe listed Tuesday and Thursday SPXW options from April 18 and May 11, 2022 respectively. They first expired on April 26 and May 19. Every weekday then had an expiry, which gives a natural experiment: the same market with and without an extra 0DTE expiry. The paper finds that the dampening comes from longer-dated positions accumulated earlier and becoming 0DTEs, not from trading on the expiration day.

Question 4

A dealer is short 1,000 of the chapter's 6,012-strike calls and spot sits at 6,000 all day. Which way does it trade between 1:30 and 3:30, and how much?

Answer

Short calls are short delta, so it opens long 31,300 share-equivalents as its hedge. Charm pulls the calls' delta from 0.216 to 0.039, so its hedge must shrink by 17,700, which it sells. This is the mirror of the worked example's dealer, who is long the calls and buys.

Question 5

In the Dealer Mechanics Lab's account, what would turn 0DTE from a stabilizing force into a destabilizing one? What do the flow data add?

Answer

A flip in the direction of retail flow from selling premium to buying it, for example through aggressive call buying in a sustained rally. Dealers would then be net short 0DTE gamma, with hedging that buys rallies and sells dips. The flow data change the premise. Customers' buying and selling are about balanced. The identifiable retail slice was already a net buyer. The dealers' long gamma comes mainly from longer-dated positions that become 0DTEs. So watch the balance of the flow and those older positions, not the retail share of volume.