Real SPX data + historical VIX backtest (≥95% within ±0.5 pts) #31

Scope

Split out of #3. The VIX math implementation + synthetic validation shipped in #30 (math RMSE ~6e-4 across 10–50% IV sweep). This issue tracks the real-data half of the original #3 acceptance criterion: ≥95% of historical days within ±0.5 pts of the published VIX.

Tasks

1. Source SPX historical option chain data. Candidates:
   • CBOE DataShop (free sample + paid bulk)
   • Wharton WRDS (academic access)
   • OptionsDX (paid commercial)
2. Source published VIX historical series. CBOE daily closes (free); intraday via VIX futures replica or DataShop.
3. Wire data loaders into research/vix-spx-replication.ipynb §13.
4. Run per-date backtest loop over a 30+ trading day window using the existing compute_vix(...) driver.
5. Validation report: histogram of |residual|, RMSE, days within ±0.5, outlier table (date, near/next expiries, strip sizes, K₀, F, σ²_1, σ²_2).

Acceptance

• ≥95% of trading days within ±0.5 pts
• Outlier table populated with diagnostics for each missed day
• RMSE printed and committed in executed notebook

Blocked by / depends on

• Notebook: replicate VIX on SPX historical, match ±0.5 pts #3 (merged): math impl + synthetic validation

Why this is split

The math correctness and the data-pipeline plumbing are independent failure modes. Synthetic validation already pins down the arithmetic. Real-data work is mostly data-engineering (sourcing, schema mapping, dividend handling, stale-quote filtering) and deserves its own diff.