fundamental_arb dossier — does Black-Scholes fair value beat Polymarket price-threshold markets OOS, net?

Status: INSUFFICIENT_DATA (pre-registered 2026-09-13, before any result was computed; result recorded 2026-09-13).

Pre-registration

Frozen with the G4 checks in tests/g4/. Nothing below may change after a result exists; a change means a new, separately registered hypothesis.

Hypothesis. For Polymarket markets that ask whether an asset's price will be above, below, or touch a strike by a date, a Black-Scholes fair probability (archived fundamental_arb pricer, realized volatility) identifies mispriced YES prices. Taking the model's side when the gap is large earns a positive net return out of sample and beats a no-skill benchmark under the same costs.

This is a limited test. Volatility is realized volatility for every asset. The archived bot preferred ATM implied volatility for equities; that variant is not tested here.

Universe.

• Markets parsed by the archived parser archive/oddsoddy/strategies/fundamental_arb/fundamental_arb_strategy/scanner.py::parse_market, imported verbatim.
• endDate between 2026-04-10T00:00:00Z and 2026-08-21T09:07:27Z, closed true, and a clean resolution: oddsx.data.markets.resolve_outcome gives YES = 0 or 1.
• Sides above, below, touch_above, touch_below. between is excluded (the archived config disabled it).
• Symbols: BTC/USD, ETH/USD, SOL/USD, AAPL, MSFT, GOOGL, AMZN, NVDA, TSLA, META, SPY.
• Strike sanity: 0.5 ≤ strike / spot at decision ≤ 2.0. This removes index-level strikes mapped to SPY and non-price "index" markets.

Decision time. One decision per market.

• t_dec = max(first_trade + 1 hour, end − 24 hours).
• Skip the market if end − t_dec < 12 hours (the archived min_hours_to_resolution).
• Skip the market if no YES-side trade priced it in the hour before t_dec.

YES price at decision. Price of trades in [t_dec − 60 min, t_dec), weighted by token_amount.

• YES is the first token in clobTokenIds.
• A trade whose outcome token is the second token is converted to YES price as 1 − price.

Model inputs.

• spot: the close of the last Alpaca 1-minute bar that ended at or before t_dec. Crypto uses BTC/USD, ETH/USD, SOL/USD; stocks use the SIP feed with raw (unadjusted) prices.
• sigma: annualized standard deviation (ddof=1) of daily log returns between the closes of Alpaca daily bars that started within the 30 days before t_dec and ended at or before t_dec (no partial bar); × √365 for crypto, × √252 for stocks.
• T: (end − t_dec) in days / 365.25.
• r = 0.05.
• p_model comes from the archived pricer: bs_prob_above (above), 1 − bs_prob_above (below), bs_prob_touch_above, bs_prob_touch_below.

Signal. edge = p_model − yes_price.

• Buy YES if edge > 0.08.
• Sell YES (buy NO) if edge < −0.08.
• Otherwise no bet.
• 0.08 is the archived bot's 6% edge plus its cost buffer. It is fixed a priori, not tuned on TRAIN.

Returns. Hold to resolution, $1 notional per bet.

• Buy at price p: (1 − p) / p if YES resolves, otherwise −1.
• Sell at price p: p / (1 − p) if NO resolves, otherwise −1.

Costs. oddsx.research.validation cost model, spread 0.02.

• fee_rate from the market's fee flags: feesEnabled false → 0.0; crypto_fees_v2 → 0.07; finance_prices_fees or tech_fees → 0.04; any other enabled fee type → 0.05.

Split. Calendar split on t_dec: TRAIN before 2026-07-01T00:00:00Z, TEST on or after it. TRAIN is reported, never used to choose anything.

Benchmark. The favorite null on the same decision set and costs. Buy YES when yes_price ≥ 0.5, otherwise sell YES. edge_vs_naive = strategy TEST mean net − benchmark TEST mean net.

Verdict rule (TEST, pooled).

• INSUFFICIENT_DATA if TEST has fewer than 200 bets.
• VALIDATED only if all three hold: mean net > 0, edge_vs_naive > 0, and the 95% lower bound of mean net > 0. The lower bound comes from a cluster bootstrap: clusters are (symbol, end), 2000 resamples, seed 7.
• FALSIFIED otherwise.

Also reported (no effect on the verdict).

• Per-cohort results by asset type and side.
• Median vs mean net return.
• The top-1% |net PnL| share.

Promotion. A VALIDATED verdict does not move anything into strategies/. Promotion is a separate operator decision.

Results

Computed by research/hypotheses/fundamental_arb/run.py on runs/g4/decisions.parquet (commit 34f1db2). Numbers are copied from registry/results/fundamental-arb.json and runs/g4/universe.json.

Universe accounting. 106,318 markets parsed in the window; 3,005 kept (one decision each). Exclusions:

Kept decisions by t_dec month: April 176, May 1,507, June 1,230, July 83, August 9. By cohort: crypto|above 918, crypto|touch_above 1,296, stock|above 786, stock|touch_above 5. No below or touch_below market survived the filters.

TRAIN vs TEST (pooled, $1 per bet, net of costs unless stated).

TEST cohorts (reported, no vote). crypto|above: 0 bets. crypto|touch_above: 11 bets, mean net −0.7536. stock|above: 4 bets, mean net −0.4321.

Tails. In TEST the median bet loses the whole stake (median net −1.03) and the mean is −0.67. In TRAIN the median is well below the mean (+0.17 vs +0.47) and the largest 1% of bets carry about 22% of absolute PnL, so the TRAIN mean leans on a few large winners.

Caveats.

• Limited test: realized volatility for every asset. The archived bot's ATM implied volatility for equities was not tested.
• TRAIN never votes. Its positive numbers (+0.47 mean net, +0.49 edge vs the favorite null) chose nothing and are not evidence the edge holds out of sample.
• TEST has only 15 bets from 92 decisions, far below the 200-bet floor. The TEST numbers are negative, but 15 bets cannot support a verdict in either direction.
• The ≥12-hour rule removed most markets (66,064 of 106,318 parsed): every market with less than 12 hours between decision time and end. The kept set is the minority of longer-dated markets. The split of those exclusions by asset is not recorded in runs/g4/universe.json.
• Decisions thin out sharply after June (92 in July–August against 2,913 before). The cause was not investigated here.

Verdict

INSUFFICIENT_DATA

The frozen rule needs at least 200 TEST bets, and TEST produced 15, so the out-of-sample question stays open: neither validated nor refuted. Nothing moves into strategies/.

Follow-up: fundamental_arb_short (goal G4b) is a separate hypothesis with its own pre-registration. It decides 1 hour before end instead of 24 (at least 30 minutes to resolution), so it can include the short-dated markets this rule excluded. It does not change or re-run this verdict.