SPX M15 Day-Type · Net VEX Intensity at the Opening Minute

Opening-Minute Vanna Exposure and Same-Session Day-Type Realization in S&P 500 Index Options

Working paper for review. Not peer-reviewed; not investment advice. For informational purposes.

Abstract

We study whether opening-minute vanna exposure structure in the S&P 500 (SPX) index option chain is associated with same-session realized day type measured on M15 ES futures candles. Using 1,960 row-observations across 490 trading sessions and a 20-session prior-only normalization window, we document four results. First, a percentile-ranked net VEX intensity gradient is associated with large-expansion realization in a monotonic and economically large fashion in the primary full-day endpoint: pooled across the 09:31-09:34 ET feature windows, the LOW intensity cohort realizes 23.77% large-expansion days (n=648), MID 13.00% (n=777), and HIGH 9.91% (n=535). Cohen's h on the LOW-vs-HIGH contrast is 0.39 (medium); a session-cluster bootstrap places the LOW-minus-HIGH gap at 13.86 percentage points with a 95% interval of [6.30, 21.24], and a session-level permutation test gives p=0.0010. The LOW-vs-HIGH separation also survives the post-09:45 sensitivity outcome, although the sensitivity endpoint is better described as LOW-vs-rest rather than a fully monotonic three-bucket result. Second, unlike on a parallel small-cap dataset, the signed direction of net VEX carries a modest secondary tilt on this rail: NEGATIVE VEX realizes 18.95% large-expansion days (n=855) versus 13.21% for POSITIVE VEX (n=1,105), a pooled gap of 5.74 percentage points with a session-cluster bootstrap interval of [0.57, 10.86] and a permutation p-value of 0.0302. Third, the relation between net VEX intensity and true-balance realization is non-monotonic, with the MID cohort registering the highest true-balance rate (24.58%), HIGH next (18.50%), and LOW lowest (13.89%). Fourth, a partially-controlled logistic specification including prior-day realized range, opex-cycle bucket, prior-session expansion state, GEX sign and magnitude, IV-percentile bucket, and day-of-week retains a positive standardized net VEX intensity coefficient (beta = +0.29). The dominant covariate is the autoregressive prior-day range (beta = +2.68). We interpret the stable expansion result as consistent with a cross-derivative dealer-hedging interpretation, although the controls are not yet sufficient to identify it. The SPX VEX-sign tilt is a research lead worth following up under joined controls; we do not promote it to a directional claim.

Keywords: index options, vanna exposure, dealer hedging, intraday range, day-type taxonomy, S&P 500.

1. Introduction

The S&P 500 index option complex is the deepest and most liquid venue for studying the interaction between aggregate option-market positioning and realized behavior in the underlying. It is the natural laboratory for empirical work on demand pressure (Garleanu, Pedersen, and Poteshman, 2009), net buying pressure (Bollen and Whaley, 2004), expiration-day pinning (Ni, Pearson, and Poteshman, 2005), and 0DTE intraday variance dynamics (Pearson and Sosi, 2024). Within that literature, vanna - the cross-partial derivative of delta with respect to volatility - has received less formal attention than gamma, in part because the vanna estimate is more sensitive to assumptions about the implied-volatility surface.

This paper isolates one narrow question on the SPX rail. Conditional on the opening-minute SPX option-surface state, measured at four distinct minute snapshots between 09:31 and 09:34 ET, is the same-session distribution of broad day-type outcomes different across cohorts defined by vanna-surface intensity and signed vanna direction? The empirical object is associational. It is not directional forward-looking claim accuracy.

For the publication comparison, both this SPX rail and the companion RUT rail use an identical 20-session prior-only lookback for intensity buckets and M15 range baselines, making the cross-index contrast like-for-like rather than a 20-vs-320-window artifact.

We make four contributions. First, we document a stable, monotonic, and economically large gradient of large-expansion realization in net VEX intensity across the primary full-day endpoint; the post-09:45 sensitivity check preserves the LOW-vs-HIGH separation but not a strict three-bucket monotonic ordering. Second, we document a modest but separable VEX-sign tilt - NEGATIVE VEX is associated with elevated large-expansion realization relative to POSITIVE VEX - that we treat as a research lead rather than a directional law. Third, we report a non-monotonic relation between net VEX intensity and true-balance realization, with the MID cohort dominating, and discuss what this pattern can and cannot support. Fourth, we report a partially-controlled logistic diagnostic in which the standardized net VEX intensity coefficient remains positive after the autoregressive prior-day range, the opex-cycle bucket, the prior-session expansion state, GEX sign and magnitude, the IV-percentile bucket, and day-of-week effects are held fixed.

Section 2 describes the data. Section 3 specifies the day-type taxonomy and prior-only baselines. Section 4 lays out the inferential plan. Sections 5-7 report primary results, post-09:45 sensitivity, and subsample stability. Section 8 reports the partially-controlled logistic. Section 9 discusses interpretation. Section 10 concludes.

2. Data

2.1 Sample

The feature side is the SPX_NATIVE option chain at four opening-minute snapshots per session: OPENING_0931, OPENING_0932, OPENING_0933, and OPENING_0934 ET. After the prior-only normalization gate, sample-coverage gate, and futures-session completeness gate, the design matrix contains 1,960 row-observations across 490 trading sessions. Each session contributes up to four observations; the within-session clustering is addressed in Section 4.

2.2 Features

The two opening-minute features of interest are net VEX intensity and VEX sign. Net VEX intensity is a prior-only percentile-ranked intensity measure of the vanna surface: at each timestamp the absolute net vanna exposure of the SPX chain is referenced against its empirical distribution across the prior 20 sessions and assigned to a LOW (bottom prior-ranked bucket), MID, or HIGH (top prior-ranked bucket) bucket using prior-only cutpoints. VEX sign is the signed direction of the net VEX integral at the same snapshot; the two cohorts are kept separate, and negative VEX is not collapsed into low intensity.

Auxiliary controls used in Section 8 are: GEX sign, GEX magnitude bucket, IV-percentile bucket, opex-cycle bucket (0DTE_WEEKLY_OPEX / WEEKLY_OPEX / MONTHLY_OPEX / OTHER), days-to-opex, prior-session expansion state, prior-day realized range (as a percentage of prior baseline), and day-of-week.

Open-interest coverage is retained as a chain-data quality diagnostic and is not used as a positioning-intensity control. Total open interest, VIX regime, and scheduled event-day flags are not joined to this design matrix and are listed in the data roadmap (Section 9).

2.3 Outcome

Throughout the paper, the headline binary endpoint is LARGE_EXPANSION only: a same-session M15 range multiple >= 1.5 versus the prior-only session-range baseline. MODERATE_EXPANSION is retained as a descriptive day-type class, but it is not counted in the headline event numerator.

The outcome rail is the ES M15 futures candle series. Each session is classified using the M15 range multiple (realized range scaled by a prior-only 20-session baseline) and the close-location coordinate:

The headline binary endpoints are LARGE_EXPANSION (expansion event) and TRUE_BALANCE (compression event). The unconditional day-type distribution is:

The unconditional large-expansion base rate is 15.71%. The binary-event contrasts below are read against this base, not against the broader "any expansion" rate of 37.14%.

3. Day-Type Taxonomy and Prior-Only Baselines

The taxonomy thresholds (1.5, 1.1, 0.8, [0.25, 0.75]) are fixed ex ante and are not optimized within the sample. The 20-session prior-only baseline is the binding sample-construction constraint and is the same lookback used by the companion RUT rail. Shorter windows would not provide a stable prior baseline; longer windows would reduce the usable sample without changing the conceptual target. Cross-window robustness, reported in Section 5, is the within-design analog of a lookback sensitivity test.

4. Inferential Plan

The plan is three-layered and pre-specified.

The first layer is the conditional cross-tab. For each opening window we report the binary event rate of LARGE_EXPANSION and TRUE_BALANCE separately by net VEX intensity bucket and by VEX sign cohort, with Wilson 95% confidence intervals for each cell.

The second layer is the pooled-across-windows summary. We treat the pooled estimates as descriptive summaries after verifying that the cross-window direction holds at each of the four opening minutes individually. Effect sizes (Cohen's h) are computed on pooled rates. As a reviewer-facing robustness layer, we also compute session-cluster bootstrap intervals for the pooled cohort gaps and a session-level permutation test that shuffles session outcomes across fixed opening-window feature rows. These tests preserve the within-session dependence created by four rows per trading day.

The third layer is a partial logistic specification. The pre-specified specification regresses the binary endpoint on a standardized net VEX intensity percentile, VEX sign indicator, GEX sign and magnitude indicators, IV-percentile-bucket indicators, opex-cycle-bucket indicators, days-to-opex, prior-session expansion state, prior-day realized range, and day-of-week indicators. We treat the coefficients as a partial decomposition rather than as causal estimates because four controls we believe matter - total open interest, VIX regime, event-day flags, and a richer opex calendar - are absent from this design matrix.

5. Primary Results

5.1 Large expansion by net VEX intensity

The cell-level event-rate table:

Pooled across windows:

The pooled cohort arithmetic reconciles to the unconditional base rate: 154 + 101 + 53 = 308 large-expansion rows, and 648 + 777 + 535 = 1,960 total rows, matching the 15.71% base rate reported in Section 2.3.

The monotonicity LOW > MID > HIGH is preserved at every individual opening window. The LOW-vs-HIGH gap is 13.86 percentage points pooled (Cohen's h = 0.39, medium). The session-cluster bootstrap interval is [6.30, 21.24] percentage points and the session-level permutation p-value is 0.0010. The LOW-vs-MID gap is 10.77 percentage points; the MID-vs-HIGH gap is 3.09 percentage points. The dominant separation is between the LOW cohort and the rest of the sample, which is itself a fact worth noting: the SPX gradient is not best described as a clean monotonic three-bucket continuum but as a sharp LOW-versus-not-LOW separation with a smaller MID-versus-HIGH refinement.

5.2 Large expansion by VEX sign

Pooled: NEGATIVE 162/855 (18.95%); POSITIVE 146/1,105 (13.21%). The pooled gap is +5.74 percentage points in the direction that practitioner narratives sometimes attribute to vanna sign. Each of the four windows preserves the same direction. Cohen's h on the pooled contrast is 0.16, which is small. The session-cluster bootstrap interval is [0.57, 10.86] percentage points and the session-level permutation p-value is 0.0302. The result is directionally stable across windows and different from zero under this finite-sample check, but the magnitude is roughly half the net VEX intensity gradient and noticeably smaller compared to the Russell 2000 study. We therefore promote the result to "stable directional tilt" rather than "directional law." Section 8 reports the partial-logistic coefficient on VEX sign as a negative coefficient on the POSITIVE indicator; that coding means the adjusted sign is still NEGATIVE-higher, but the magnitude is small once net VEX intensity and the autoregressive prior-day range are held fixed.

5.3 True balance by net VEX intensity

The pattern is non-monotonic: MID is the highest, HIGH second, LOW lowest. This rules out a clean "intensity-as-compression-pressure" reading for the SPX true-balance endpoint. A LOW intensity surface is the lowest realization rate for true balance, as a simple structural reading would suggest. But the highest true-balance realization rate sits in the MID cohort rather than HIGH. We discuss candidate mechanisms in Section 9.

6. Sensitivity: Post-09:45 Outcome

The post-09:45 sensitivity outcome on net VEX intensity:

The LOW-vs-HIGH gap survives with a session-cluster bootstrap interval of [3.44, 19.27] percentage points and a session-level permutation p-value of 0.0072, but the MID/HIGH ordering inverts relative to the primary outcome. The honest description is therefore a sensitivity-confirmed LOW-vs-HIGH separation, not a strict post-09:45 monotonic replication. The primary versus sensitivity agreement on the binary LARGE_EXPANSION endpoint is 1,904 of 1,960 paired rows (97.14%):

The sensitivity-side preservation of the LOW-vs-rest gap is, in our view, the strongest evidence in the paper against a mechanical opening-bar interpretation. We discuss the small MID/HIGH inversion in Section 9 as a candidate signature of cohort-composition rather than a substantive reversal.

7. Subsample Stability

The 1,960-row design matrix decomposes into two cohorts: 1,504 rows from the original collection and 456 rows from a subsequent overnight collection. The two cohorts share the protocol but were collected at different periods.

For net VEX intensity -> large expansion, both cohorts produce HIGH < LOW. The combined-sample finding in Section 5.1 is robust to cohort subsampling.

For net VEX intensity -> true balance, both cohorts produce HIGH > LOW. The non-monotonic MID-dominated pattern reported in Section 5.3 is therefore robust to cohort subsampling, even though it is itself a more complicated pattern than the simple monotonic gradient.

For the post-09:45 sensitivity expansion endpoint, the two cohorts disagree on direction. The original cohort produces HIGH < LOW (consistent with the primary finding). The new cohort produces HIGH > LOW. The combined-sample direction (HIGH < LOW) in Section 6 is therefore weighted by the original cohort. We classify the sensitivity expansion result as direction-consistent in the combined sample but cohort-mixed at the subsample level, and we report it as a robustness caveat rather than a headline result.

For the VEX-sign tilt on large expansion, both cohorts produce NEGATIVE > POSITIVE. The Section 5.2 tilt is therefore robust to cohort subsampling.

8. Partial Logistic Diagnostic

Sign-convention audit note: net_vex_intensity_percentile_20 is not inverted; higher values mean a higher prior-only rank for net VEX intensity. The positive adjusted coefficient in the partial logistic is a continuous, covariate-conditioned diagnostic, not the same estimand as the LOW-versus-HIGH bucket comparison. It should therefore be read as an appendix-level robustness diagnostic rather than as a monotonic restatement of the headline bucket result.

We fit a logistic specification of the headline LARGE_EXPANSION endpoint on standardized continuous net VEX intensity percentile, VEX sign indicator, GEX sign and magnitude indicators, IV-percentile-bucket indicators, opex-cycle-bucket indicators, days-to-opex, prior-session expansion state, prior-day realized range, and day-of-week indicators. The standardized coefficients in descending absolute magnitude:

Three observations follow.

First, the dominant covariate is the autoregressive prior-day realized range. This is consistent with the well-known volatility-clustering literature and does not require an option-positioning interpretation. The remaining coefficients should be interpreted conditional on this very large autoregressive baseline.

Second, the net VEX intensity percentile retains a positive standardized coefficient (+0.29) after the autoregressive baseline, the opex cycle, the prior-session expansion state, GEX structure, and day-of-week effects are held fixed. The conditional effect is attenuated relative to the unconditional cross-tab in Section 5, which is the expected pattern when a partial control absorbs some - but not all - of the bucket-level variation. The conditional association survives the partial decomposition.

Third, the VEX-sign coefficient is negative on the POSITIVE indicator (VEX_POSITIVE = -0.25), meaning POSITIVE VEX is associated with less large-expansion realization after controls; equivalently, the adjusted sign is consistent with the unconditional NEGATIVE > POSITIVE tilt. The conditional magnitude is comparable to several day-of-week effects, which is one reason we resist promoting the Section 5.2 tilt to a directional law. The unconditional 5.74-percentage-point gap is partly attributable to the structure of the partial control set; what remains after controls is a smaller, but still directionally stable, tilt.

GEX-sign-positive emerges as a small positive covariate (+0.30) on this rail, smaller than the same coefficient on the Russell rail in a companion exercise. The signed-GEX coefficient is itself a research lead worth carrying forward into the joined-controls design matrix.

The post-09:45 sensitivity logistic produces qualitatively similar coefficients on net VEX intensity (+0.29), the prior-day range (+2.70), and prior-session non-expansion (-0.63). The pattern is internally consistent: the partial logistic identifies essentially the same standardized association in the primary and sensitivity specifications, which is the strongest robustness research feature available within this design.

As a post-hoc reviewer diagnostic, we also refit the Tier 1 expansion specification with a statsmodels GEE-binomial model grouped by session. The net VEX intensity coefficient remains positive in both SPX expansion models: +0.525 on the primary endpoint with grouped 95% CI [0.111, 0.938] and p=0.0128; +0.533 on the post-09:45 endpoint with grouped 95% CI [0.115, 0.952] and p=0.0125. These GEE coefficients are not numerically comparable to the deterministic regularized coefficients above, but they address the reviewer concern that the four opening-window rows per session create non-independent observations.

9. Discussion

9.1 The stable result

The stable result on this rail - a monotonic decrease in large-expansion realization across LOW -> MID -> HIGH net VEX intensity buckets, with the dominant separation between LOW and the rest of the sample - is consistent with a structural cross-derivative dealer-hedging interpretation. A LOW intensity reading describes a vanna surface whose absolute magnitude sits in the bottom prior-ranked bucket of its recent 20-session distribution; the cross-derivative hedging pressure imposed by the dealer book is correspondingly small relative to its own historical baseline, and the futures-side realized range is freer to extend. The mechanism is the cross-derivative analog of the gamma-pinning channel (Ni, Pearson, and Poteshman, 2005).

The SPX gradient is steeper than the Russell analog (Cohen's h = 0.39 versus 0.29). Two candidate mechanisms are worth listing without adjudication. First, SPX has a deeper option chain and a finer strike grid than RUT; the vanna integral on a fine grid may be a less noisy estimate of dealer-book convexity than the same integral on a coarse grid, and the SPX bucket assignment may therefore have higher research feature-to-noise. Second, the SPX chain may absorb a larger share of demand-pressure-driven flow per unit of realized intraday range than RUT; the cross-derivative channel may simply transmit more strongly on the deeper rail.

9.2 The VEX-sign tilt

The 5.74-percentage-point pooled tilt by VEX sign (NEGATIVE > POSITIVE) is directionally stable, present in both subsamples, and survives a primary-versus-sensitivity check. After the partial logistic absorbs the autoregressive prior-day range, the opex bucket, the prior-session expansion state, and GEX structure, the conditional sign coefficient is smaller and in the same direction but is comparable in magnitude to ordinary day-of-week effects. The honest reading is that the SPX VEX-sign cohort tilt is a real but secondary feature of the data. It is consistent with the practitioner intuition that negative vanna positioning on the SPX surface is associated with elevated range realization, but it does not yet support a directional-law statement because we do not have the missing controls (VIX regime, total OI, event days, richer opex calendar) that could absorb it.

9.3 The non-monotonic true-balance pattern

True-balance realization is highest in the MID cohort (24.58%) and lowest in the LOW cohort (13.89%), with HIGH at 18.50%. The non-monotonicity is robust to cohort subsampling (Section 7). One candidate interpretation is that the dealer-hedging cross-derivative channel imposes a concentrated compression pressure that is strongest in the middle of the prior-only intensity distribution, where the bucket boundary is most informative about the dealer book's intermediate state. Another is that HIGH intensity sessions overlap disproportionately with event-driven or scheduled-news days that produce directional closes rather than balanced closes, depressing the HIGH-cohort true-balance rate below the structural forecast claim. We cannot adjudicate without joining the event-day calendar. The pattern is real; the interpretation is open.

9.4 The role of the autoregressive prior-day range

Across both primary and sensitivity logistic specifications, the standardized coefficient on prior-day range is approximately +2.7, an order of magnitude larger than any single option-side coefficient. This is the volatility-clustering effect documented in a large literature. Two notes follow.

First, the option-side coefficients in Section 8 are correctly interpreted as the marginal contribution of opening-minute option structure above and beyond the autoregressive baseline. They are not the unconditional cross-tab values reported in Section 5. The attenuation is expected and is not a refutation of the cross-tab.

Second, future work should consider whether the cross-derivative channel is meaningfully separate from a volatility-clustering channel or whether it is a parallel observation of the same underlying state. The present design cannot adjudicate between these two readings.

9.5 Data roadmap

Control caveat: OI coverage is treated only as a data-quality diagnostic, not as true total open interest. VIX regime, richer event-day flags, and full OI controls remain future-work controls rather than publication-blocking requirements for the narrow descriptive claim.

The most valuable next step is a joining operation that brings four missing controls onto the design matrix:

A second contribution that does not require new data is a formal cross-lookback robustness exercise comparing 20, 40, and 60-session prior-only windows on the headline endpoint. The cross-window stability reported in Section 5 is the within-design analog and supports the lookback choice, but a formal exercise is preferable.

9.6 What this study does not establish

This study does not establish causality, actionable trading edge, dealer intent, or directional forward-looking claim evidence. It establishes a stable cohort-level conditional association between an opening-minute SPX option-chain summary and a same-session range outcome, and it offers a partially-controlled decomposition consistent with the structural literature.

10. Conclusion

In S&P 500 index options, the percentile-ranked absolute intensity of the opening-minute net vanna exposure is associated with same-session large-expansion realization in a monotonic and economically large fashion in the primary endpoint. The relation is stable across all four opening minutes, survives a post-09:45 LOW-vs-HIGH sensitivity check, remains direction-consistent across two subsamples collected at different periods, and survives a partially-controlled logistic specification that holds the autoregressive prior-day range, the opex bucket, the prior-session expansion state, and GEX structure fixed. The signed direction of net VEX carries a small but directionally stable additional tilt: NEGATIVE VEX cohorts realize more large-expansion days than POSITIVE VEX cohorts by approximately 5.7 percentage points. The relation to true-balance realization is non-monotonic, with the MID cohort dominating. The natural next step is to join total open interest, VIX regime, event-day flags, and a richer opex calendar to the design matrix and repeat the partially-controlled logistic. The cross-derivative dealer-hedging interpretation of the stable expansion result is consistent with the data; the controls are not yet sufficient to identify it.

References

See companion Russell paper for shared references. Additional citations specific to the SPX discussion:

Christoffersen, P., Goyenko, R., Jacobs, K., and Karoui, M. (2018). Illiquidity premia in the equity options market. Review of Financial Studies, 31(3), 811-851.

Appendix A: Additional diagnostic dashboard figures

The following figures are retained as working-paper diagnostics. They should not lead the public Substack body.