Variance Risk Premium & Variance-Swap Replication (SPX)

Replicates a 30-day SPX variance swap from option strips (model-free implied variance, CBOE VIX methodology), validates the synthetic index against the live VIX, measures the variance risk premium with strictly forward-looking realized variance, and backtests a cost-aware short-variance carry.

Approach & findings

• Replicated 30-day implied variance from SPX option chains (Databento OPRA, 2017–2023, 1,676 trading days): 0.568 vol-point mean absolute error and 0.9909 correlation against the real CBOE VIX, with no regime where the replication breaks down (per-year MAE 0.32–0.76).
• Validation surfaced and fixed three real data bugs: stale-tick corruption of the put-call-parity forward (min-volume gate), invalid time-interpolation when monthly expiries fail to straddle 30 days (dates dropped, not extrapolated), and exchange reuse of instrument IDs (bars re-keyed by their own embedded symbol).
• Measured the VRP at +3.75 vol points on average (positive 83.7% of days) with strictly forward-looking realized variance; regime breakdown shows it thinning to +2.3 in 2020/2022, and single days as negative as −72.3 vol points in Feb 2020 — implied vol did not come close to pricing COVID in advance.
• Backtested a rolling short-variance carry with per-entry 1/n vega-notional sizing, 10 bps entry costs, and a backward-looking realized-vol tail stop: net Sharpe 1.84, 18.0% CAGR, +221% total, with a −70.6% max drawdown concentrated entirely in the COVID window — reported as the structural limitation of a tail stop, not hidden.
• Interactive Streamlit dashboard with live-recomputable costs/sizing/estimator controls; the fixed 30-day tenor control is disabled rather than silently faked.

Results

VIX correlation

0.9909

Mean abs error

0.568 vol pts

Net Sharpe / CAGR

1.84 / 18.0%

Mean VRP (83.7% days > 0)

+3.75 vol pts