Expiry-Driven Reconfiguration of the Options Constraint Field

Research Status

Active research. Not part of the current production forecast model. Not a validated trading strategy.

This research program studies a simple mechanical event.

Option contracts expire on known dates. When a large expiry disappears from the next observable option-chain snapshot, the distribution of open interest across strikes and expiries changes. That change can move aggregate structural measurements such as the open-interest centroid.

The central question is:

Does a scheduled change in the options matrix produce a measurable and delayed response in the underlying price?

The work began with a visual observation. Aggregate open-interest centroids appeared to move in a repeated sawtooth pattern as large monthly and weekly expiries rolled off and later expiries accumulated new open interest.

The idea was initially described too strongly. Early notes treated centroids as price attractors and some expiry moves as direct causal proof. Later tests forced a narrower and more defensible interpretation.

The surviving result is not that price must move toward one centroid.

The surviving result is that expiry creates a scheduled reconfiguration of the measured options field, and the market's response to that reconfiguration can be studied as a systems-identification problem.

The Measured Objects

The research uses several structural measurements.

KOI

KOI is an open-interest-weighted strike centroid.

For one expiry, it summarizes where open interest is concentrated across strikes. An aggregate form, often called KOI_all, combines information across expiries.

KOI does not identify trader intent.

It does not show who bought or sold the contracts. It does not show the sign of dealer exposure. It is a location measurement for contract inventory.

K-Star

K-star is a volatility-sensitive structural center.

It is related to the location of the implied-volatility surface rather than only the location of open-interest inventory.

The research initially treated K-star as a possible equilibrium basin. Later lead-lag and event studies did not support K-star as a clean forcing variable. It remains useful as a structural reference.

Expiry Share

Each expiry contributes a fraction of the total observed open interest.

A large expiry can materially change an aggregate centroid when it disappears. The size of the effect depends on both its weight and its location relative to the remaining distribution.

Gamma And Near-Dated Inventory

Near-dated contracts can have strong gamma sensitivity.

Early hypotheses treated gamma as the direct driver of expiry impulses. Later tests showed a more complicated relationship. Gamma-related measurements helped describe movement amplitude and market state, but no simple rule such as "more gamma means a larger directional move" survived.

The Timing Problem

The most important correction in this research involved the definition of the expiry step.

A daily snapshot taken on an expiry date still contains the contracts expiring that day. The first daily snapshot that no longer contains those contracts is the next trading day's snapshot.

Therefore, the observable field change is:

observed post-expiry KOI change
= KOI_all(t + 1) - KOI_all(t)

where:

• t is the expiry-day snapshot.
• t + 1 is the next trading-day snapshot.

An earlier version used:

KOI_all(t) - KOI_all(t - 1)

That measured movement into the expiry date while the contracts still existed. It mixed pre-expiry drift, contract repricing, and the active pinning environment. It did not isolate removal of the expiry.

Correcting the timing definition resolved an apparent sign contradiction.

For example, removing a below-average expiry should mechanically raise a weighted average, all else equal. The earlier label could classify such an event incorrectly because it measured the wrong side of the boundary.

Why The Observed Post-Step Is Not Fully Ex-Ante

The corrected observable has another limitation.

KOI_all(t + 1) is only known after the next snapshot exists. It includes:

• Removal of the expired contracts.
• Any new contracts or new open interest visible on the next day.
• Changes in the remaining option matrix.
• Possible effects of a weekend for Friday expiries.

Therefore, the observed post-expiry KOI change is a useful research label, but it is not itself a pre-event trading signal.

A genuinely ex-ante signal requires a mechanical estimate based only on the expiry-day snapshot.

A first-order estimate can remove the expiring inventory mathematically from the current weighted distribution. That estimated change is knowable before the contracts disappear from the feed.

The next research requirement is to compare:

mechanically estimated KOI removal at t

with:

observed KOI_all(t + 1) - KOI_all(t)

Only after that comparison can the expected field change be called a validated pre-event measurement.

A Controls-Based Framing

Expiry gives the research a useful system-identification structure.

The scheduled disappearance of a known contract set acts like a parameter step in the measured options field.

The components are:

• Input: removal of expiry-specific open-interest mass.
• State: the resulting options-field configuration.
• Output: subsequent price behavior.
• Delay: the time between the field change and the measured price response.
• Gain: the size of the price response relative to the structural change.
• Damping: how quickly the response decays or becomes contaminated by later events.

This framing led to event-aligned impulse-response plots.

For each expiry event, the series were aligned around the expiry date. Changes in KOI, K-star, gamma-related measurements, and spot were measured relative to a pre-event or expiry-day baseline.

The purpose was not to fit a mechanical oscillator equation.

The purpose was to ask a direct empirical question:

When the observed options field changes at expiry, what does the average market path look like before and after the event?

[Insert pooled KOI and spot impulse-response chart]

Suggested caption: Pooled expiry events aligned to the expiry boundary. The KOI panel shows the average measured field reconfiguration. The spot panel shows the smaller and more variable average underlying response. Shading represents uncertainty around the estimated mean response, not the range of individual outcomes.

Multi-Asset Pooled Event Study

The corrected pooled study contained 571 expiry events across the analyzed symbol set.

The observed post-step split was:

• 264 post-step-up events.
• 307 post-step-down events.

This was a major improvement over an earlier SPY-only split that produced a very small downside sample.

The earlier small sample was not the true frequency of expiry events. It was a consequence of:

• Using one symbol.
• Using the pre-expiry change definition.
• Applying strict event filters.
• Looking only at one dominant expiry at a time.

After the timing correction and multi-symbol pooling, the event count became large enough to study average shape and asymmetry.

What The Impulse Responses Supported

The pooled research supported several modest conclusions.

Expiry Reconfigures The Measured Field

The KOI path showed a clear average change around the expiry boundary.

This is expected. Contract inventory is being removed from the observed matrix.

The important point is that the measured change was large enough and regular enough to treat expiry as a real structural event rather than ordinary day-to-day noise.

Price Response Is Smaller And Noisier Than Field Response

The spot response was much less clean than the KOI response.

This matters.

A scheduled options-field change does not imply a deterministic price path. Price remains affected by:

• New information.
• Liquidity.
• Broader positioning.
• Volatility state.
• Existing trend.
• Other expiries.
• Overnight gaps.
• Rebalancing and hedging behavior that is not directly observed.

The Response Appears Delayed

Average spot behavior changed over the days following the expiry boundary rather than only at one instant.

The strongest effect often appeared over approximately one to three trading days in the exploratory event windows.

This supported the systems-identification framing, but it did not by itself prove causal transmission from KOI to price.

Downside And Upside Were Not Symmetric

The conditioned average paths were not mirror images.

Downside responses were often sharper. Upside responses were weaker or more diffuse.

This is plausible in equity markets, but it should not be explained through a dealer-flow story without data that directly identifies dealer positioning.

The public conclusion should remain empirical:

The observed response was asymmetric, with stronger average downside behavior in several event definitions.

Lead-Lag Analysis

Lead-lag correlations were used to compare changes in structural measurements with changes in price.

This test required careful interpretation.

Several measurements derived from the same daily option snapshot had very high same-date correlations with spot. Those same-date peaks can be mechanical because spot enters moneyness, strike selection, and other option-surface calculations.

Same-date correlation was therefore not treated as causal evidence.

The more useful question was whether one series showed a stable off-zero relationship with future price changes.

KOI changes showed the most interesting off-zero structure in the exploratory analysis. K-star and gamma-centroid locations were more contemporaneous and did not provide a clean independent directional lead.

However, the research did not retain a universal lead-lag claim. Results depended on:

• The exact step definition.
• Symbol pooling.
• Event alignment.
• Whether the analysis used levels or changes.
• How overlapping expiry events were handled.

The durable conclusion is narrower:

KOI is the most useful state variable for describing the direction of the observed field change. K-star is better treated as a reference state than a directional forcing term.

Amplitude Is A Separate Problem

The event study separated two questions:

1. What direction did the measured field move?
2. How large was the subsequent underlying move?

The research found that simple structural displacement did not explain movement amplitude well by itself.

Large |Delta KOI| did not produce a clean monotonic increase in maximum underlying movement.

Several static gamma and open-interest composites also failed to produce reliable monotonic lift.

The strongest single visual relationship came from volatility-state measurements such as relative ATR and rolling return volatility. These measurements described how much movement the market could express over a short window.

This suggested a decomposition:

• Structural measurements describe the event and field reconfiguration.
• Volatility measurements describe movement capacity.
• Trend and local geometry modify propagation.
• The full amplitude response is nonlinear.

Held-Out Amplitude Modeling

A later experiment used XGBoost with pre-event features only.

The targets included:

• Maximum absolute underlying move over days 1 to 3.
• Mean absolute underlying move over days 1 to 3.
• Sum of absolute underlying movement over days 1 to 3.
• Direction-conditioned targets.

In one held-out test, the amplitude targets produced approximate out-of-sample R-squared values of:

• 0.44 for maximum absolute movement.
• 0.42 for mean absolute movement.
• 0.41 for summed absolute movement.

The direction-conditioned targets produced negative out-of-sample R-squared.

This result is promising, but it requires careful qualification.

It supports the idea that pre-event market state contains information about movement capacity.

It does not establish a production-ready amplitude model.

The result still requires:

• Strict chronological testing.
• Leave-one-symbol-out testing.
• Stability checks across eras.
• Hyperparameter controls.
• Verification that all feature timestamps are pre-event.
• Option-level execution simulation.
• Transaction-cost and spread modeling.

The top predictors were mainly volatility and trend measurements, including rolling return standard deviation, Parkinson volatility, short trend slopes, and selected options-geometry features.

That result is internally coherent.

The field event may define the structural disturbance, while the pre-event volatility state constrains how far price can travel.

Failed Or Revised Hypotheses

"KOI Is A Price Attractor"

This language was too strong.

A centroid summarizes contract inventory. It is not a guaranteed destination.

Revised conclusion: KOI is a useful state variable for options-field location and reconfiguration.

"K-Star Gives A Clean Reversion Trade"

The average return toward K-star was slow and noisy. Other expiries entered during the holding window.

Revised conclusion: K-star may be a structural reference, not a validated entry rule.

"Gamma Directly Scales The Move"

Individual gamma variables showed useful rank relationships in some tests, but simple linear and threshold rules failed.

High-gamma regimes could also be strongly pinned and produce less directional travel.

Revised conclusion: Gamma-related variables are state descriptors. Their effect is nonlinear and conditional.

"A High-Gamma Regime Isolates Strike-Crossing Trades"

A strict high-gamma filter did not produce reliable fixed-dollar strike-crossing outcomes.

Revised conclusion: Static level filters are insufficient.

"A Large KOI Step Should Create Monotonic Amplitude Lift"

The relationship was not globally monotonic.

Revised conclusion: Directional field change and movement capacity are separate dimensions.

"The Observed Post-Step Direction Is Known Before Expiry"

It is not. The observed post-step uses the next snapshot.

Revised conclusion: A separate mechanical pre-event estimate must be built and validated.

Current Working Model

The current research model is:

scheduled expiry
    -> measurable option-field reconfiguration
    -> delayed and noisy price response

pre-event volatility and trend state
    -> conditional movement capacity

observed post-expiry KOI change
    -> research label for field direction

This is not yet a complete trading model.

The missing link is a validated ex-ante estimate of the post-expiry field change.

Next Experiments

Validate The Mechanical KOI-Removal Estimate

Compute the aggregate centroid after removing the expiring contracts from the current snapshot.

Compare that estimate with the first post-expiry observed snapshot.

Measure:

• Sign accuracy.
• Absolute error.
• Rank correlation.
• Sensitivity to new open interest.
• Differences between weekly, monthly, and quarterly expiries.

Run Chronological And Symbol-Holdout Amplitude Tests

A random or simple held-out split is not enough.

The amplitude model should be tested with:

• Early-years train, later-years test.
• Leave-one-symbol-out validation.
• Multiple market regimes.
• Fixed feature definitions and hyperparameters.

Model The Response Path, Not Only Maximum Movement

Maximum movement is noisy.

Alternative targets include:

• Mean absolute movement.
• Directional mean movement.
• Integrated movement over the event window.
• Quantile movement.
• Maximum favorable and adverse excursion.

Test Actual Options Execution

Underlying movement does not directly equal option profit.

The next phase requires preserved option-chain snapshots or a defensible pricing simulation that includes:

• Implied volatility.
• Delta and gamma.
• Theta.
• Bid-ask spread.
• Entry time.
• Exit rule.
• Strike selection.
• Days to expiry.
• Overnight gap risk.

Separate Overlapping Expiry Events

Weekly options create frequent overlapping changes.

The analysis should identify when one event window is contaminated by the next expiry.

Current Conclusion

The expiry research has established a measurable and repeatable field-reconfiguration event.

It has not established a deterministic directional trade.

The strongest supported claims are:

• Expiry changes the observed distribution of options inventory.
• Aggregate centroids record that reconfiguration.
• The underlying response is delayed, smaller, and more variable than the structural step.
• Response amplitude is state-dependent.
• Pre-event volatility and trend features contain promising information about amplitude.
• The observed post-expiry centroid change is not fully ex-ante.
• A mechanical removal estimate is the next required bridge from research label to usable signal.

That is a meaningful result.

It is also a narrower result than the earliest working notes claimed.