Webull Hybrid Lab — Does Exhaustion + Divergence Additivity Survive the Options Pivot?NULL-HYPOTHESIS STUDY

Webull Hybrid Lab · Phase 1 (paper mode) · 2026-06-17 · ~9 min read · N = 0 closed option-trades at publication · pre-registered protocol

1. Lineage — the additivity question, on a new rail

This lab descends from the Hybrid Lab (hybrid_engine.py), documented in the hybrid_v1 methodology whitepaper. That engine ran a six-stage pipeline — deterministic exhaustion prior, Kaufman-ER regime gate, a logit-space ensemble of five regime-gated features, a bounded vision-LLM fold, PAV isotonic calibration, and drawdown-braked ¼-Kelly sizing — to answer one question: whether merging two individually-weak signals (exhaustion regime, provider divergence) yields an edge larger than the sum of its parts. Its honesty commitments — an 88% logit clamp, a per-bucket Wilson lower bound, an openly-displayed identity calibrator below 25 samples — are inherited here wholesale.

The pivot's headline findings frame why additivity is the right question to re-ask on options. Finding #4 said both source regimes "contain regime information … [and] DO meaningfully shift implied-vol expectations" but produced no executable binary edge. Finding #5 adopted the project conclusion: stop monetising direction as a binary bet, and shape an options payoff around the predicted regime instead. The Hybrid Lab is where those two findings collide most interestingly — because the two component regimes make opposite volatility statements:

The exhaustion regime says "the move is overextended — expect vol contraction as it mean-reverts." The divergence regime says "the readers disagree — expect vol expansion as uncertainty resolves." When both fire at once, they are not redundant confirmations; they are a structured disagreement about the next regime.

That tension is exactly what makes the additivity question non-trivial. In the binary world the two signals could only ever vote on direction, so their vol disagreement was invisible — washed into a single bull-probability. On the options rail the disagreement becomes a selectable structure: the relative magnitude of exhaustion_score vs divergence_score tells the selector whether to lean short-vol (contraction wins), long-vol (expansion wins), or vol-neutral-directional (they cancel, leaving only the exhaustion fade direction). Findings #1 and #3 still bind: read real b off geometry, size off p_lower.

2. Method

2.1 The regime classifier — which forecast engine feeds it

The classifier is hybrid_engine.py, used unmodified as the forecast layer. It emits the §2.2 regime block with both exhaustion and divergence populated. Per the §2.3 contract, this lab's /observe response additionally echoes exhaustion_score and divergence_score as top-level fields so the page can render the two-component HUD — the user always sees the two raw inputs that drove the structure choice, never just the verdict. This is the hybrid_v1 "factors[] audit trail" discipline carried onto the options rail.

2.2 The strategy selector — the candidate set

The selector reads the relative magnitudes of the two scores and selects from the full defined-risk subset of the Periodic Table (WEBULL_PIVOT §3) — this is the only lab whose candidate set spans both the contraction and expansion families, because only the hybrid sees both signals:

The "both high" row is the additivity test's sharp edge: it routes to a defined-risk vertical that monetises the exhaustion fade direction while staying roughly vol-neutral, on the thesis that the two signals agree a regime change is imminent even as they disagree on its vol sign. With defined_risk_only=true the selector never returns a naked short-vol leg even when the contraction read dominates — the Mertonian fat-tail discipline from the hybrid_v1 CHOP-BUSTER section binds here too.

2.3 The calibration pipeline — reuse, do not reinvent

Closed trades persist on the existing paper_trade_service.py row (no parallel DB) with the §2.4 columns. The additivity question makes per-structure bucketing indispensable: /api/cv/paper/calibration?strategy_id= lets us compare the hybrid's bull_call_spread bucket against the Edge and TRAIL labs' same-structure buckets, and the hybrid's long_strangle bucket against the Divergence lab's — the only way to tell whether combining the signals beat using either alone. Wilson 95% lower bound per bucket (Wilson 1927); exhaustion_score / divergence_score are persisted in legs_json context for post-hoc additivity analysis.

2.4 The ergodic Monte-Carlo evaluation (F7)

Break-even is p* = 1/(1+b) off each structure's geometry; sizing is fractional Kelly off p_lower (F7 README — never p_hat), with the hybrid_v1 drawdown brake and losing-streak damper carried forward. The additive ergodic Monte Carlo (Peters 2019) reports time-average growth. The hybrid lab is the most exposed to finding #2's trap: combining signals can lift ensemble EV (more "confirmations" feel like more edge) while the time-average growth path stalls or worse, because the combined selector trades more often and pays more friction. A positive EV with ≤ 0 growth rate is a fail.

3. Null hypothesis & stop criterion

We reject H₀ only if, over ≥ 100 closed paper option-trades in at least one webull_strategy_id bucket, the hybrid Wilson lower bound both exceeds break-even and exceeds the matching single-lab bucket (the additivity clause):

The second condition is what makes this an additivity test rather than a fourth directional test. Beating break-even is necessary but not sufficient: if the hybrid clears p* only by routing to a structure that the Edge or Divergence lab already clears alone, then merging added nothing — the edge lived in one component, and H₀ stands. Additivity is rejected only when the combination demonstrably outperforms its best part on a ≥ 100-trade bucket.

4. What a failure to reject tells us

Per the lab's stance, a null-not-rejected result is a successful run. A sustained failure teaches:

• Additivity did not survive the venue change. If two regimes that shift IV expectations cannot, combined, fund a structure beyond what each does alone, then the binary-era hope that merging weak edges compounds them does not transfer to options. That is a clean, expensive-to-fake result that settles the hybrid program's central question on the new rail.
• The structured disagreement is real but unprofitable. The exhaustion-vs-divergence vol tension (contraction vs expansion) may be genuine signal about regime change and still not clear the friction of expressing it — finding #4's "information without executable edge," now confirmed for the combined signal.
• Defined-risk capping held under the busiest selector. The hybrid trades most often and across the widest structure set; a clean null with bankroll intact is the strongest evidence that the defined_risk_only guard plus drawdown brake contained the most active lab without a ruin path.

5. Phase 2 — must-do / must-not

Must-do:

• Reliability diagram per strategy bucket, plus a head-to-head p_lower table of the hybrid bucket vs each single-component lab's same-structure bucket — the additivity ledger made visible.
• Per-strategy theta budget — the hybrid spans both long-vol and short-vol structures; track theta_paid_usd and vega_at_entry per bucket so a contraction harvest is never conflated with a directional or expansion edge.
• Binary-payout variant — if the lab eventually routes Pocket-Option-style binaries, add the +0.8/−1.0 contract so the original binary hybrid additivity result can be benchmarked directly against the options expression.

Must-not:

• Tune the score-combination weights on n < 100. Stacking weak signals on a thin sample is how noise gets mistaken for additivity.
• Deploy capital — instrument only; capital follows a sustained friction-honest p_lower > p* that also clears the additivity clause.
• Flip defined_risk_only=false while p_lower < p* — the busiest, most structure-diverse lab is the worst place to remove the downside cap before the edge is proven.

References

1. Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option Pricing: A Simplified Approach. Journal of Financial Economics, 7(3), 229–263. (Binomial valuation across the full defined-risk structure set the selector spans; alternative to Black & Scholes 1973.)
2. Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654.
3. Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal, 35(4), 917–926. (Payoff ratio b, break-even p* = 1/(1+b); drawdown-braked ¼-Kelly inherited from hybrid_v1.)
4. Wilson, E. B. (1927). Probable Inference, the Law of Succession, and Statistical Inference. Journal of the American Statistical Association, 22(158), 209–212. (Per-bucket lower bound and the additivity comparison.)
5. Peters, O. (2019). The Ergodicity Problem in Economics. Nature Physics, 15, 1216–1221. (Time-average vs ensemble growth — the F7 objective; especially sharp for the most-active lab.)
6. Merton, R. C. (1969). Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. Review of Economics and Statistics, 51(3), 247–257. (Defined-risk preference over short-vol fat tails, inherited from the hybrid_v1 CHOP-BUSTER analysis.)
7. Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House. (Why stacked weak signals can stack noise; fragility of thin-sample additivity claims; optional.)
8. Lineage: Binary Exhaustion Lab — hybrid_v1 Methodology Whitepaper; component labs: Webull Exhaustion and Webull Divergence; binary additivity framing: WEBULL_PIVOT_STUB_PROMPT.md §1.2 & §1.4, finding 4.

Webull Hybrid Lab · Phase 1 (paper mode) · 2026-06-17 · simulation only — no capital is ever at risk. Calibration reused from paper_trade_service.py (no parallel DB). /observe echoes exhaustion_score + divergence_score for the two-component HUD. Companion instruments: Edge, Exhaustion, Divergence, TRAIL.