Realized vs implied volatility

Definition

This indicator compares what movement the options market PRICED (implied volatility, opt-implied-volatility) with what the underlying DELIVERED (realized volatility over the matching window). The spread between them — the volatility risk premium — is the single quantity that decides whether option sellers or buyers were paid over any period, and it is the platform’s core options-economics gauge.

How it works / structure

• Realized side: annualized standard deviation of daily log returns over the window (close-to-close convention; range- based estimators like Parkinson exist and are pinned when used).
• Implied side: at-the-money IV at matching tenor, or the variance-swap-style strip (VIX methodology) for a model-freer read.
• The comparison (engine-executable): IV_t(tenor) vs subsequent RV over that tenor — entered prospectively (does today’s IV overprice the future?) and retrospectively (did sellers earn the spread?); expressed as a ratio or vol-point spread, tracked as a distribution per underlying.
• What the sign means: IV persistently above subsequent RV = positive volatility risk premium — the priced compensation option sellers collect for carrying tail risk (strategy-iron-condor, strategy-strangle economics); episodes where RV explodes past IV are where sellers repay it.

When it applies

Every options strategy’s entry gate reduces partly to this comparison: premium selling wants IV rich relative to plausible RV (iv_rank is the normalized screen); long-volatility event structures want the reverse (strategy-straddle, strategy-backspread); delta-hedged P&L IS this spread realized through rebalancing (mgmt-delta-hedging).

Risk profile & failure modes

• The premium is compensation, not free money: its distribution is many small seller wins against rare violent losses — averages mislead; the tail episodes define the strategy class.
• Estimator mismatch: close-to-close RV understates gap-heavy movement; comparing it to IV (which prices the whole path) flatters sellers in gappy regimes.
• Window mismatch: comparing 30-day IV to trailing (not subsequent) RV is the common retail error — trailing RV is known; the premium is about the future.
• Single-name idiosyncrasy: index-level premium evidence transfers weakly to single names around events (earnings IV is a different animal — event-earnings).

Evidence & limits

Carr-Wu (2009) documented significantly negative variance risk premia (variance swap buyers paid) across major indexes; Bakshi-Kapadia (2003) found the same via delta-hedged option returns. The premium is among the best-documented facts in options markets — index-level, sample-period bounded, and punctuated by seller-ruin episodes. Per-name, per-period persistence is a replay question, never an assumption.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X’s 30-day ATM IV today will exceed its subsequent 30-day realized volatility” — falsified by the matched-window comparison.
• “Selling the strip where IV percentile > 80 on universe U earns positive average premium over subsequent RV this year in replay” — falsified by the replay distribution.

Cross-references

• Components: opt-implied-volatility, opt-iv-rank-percentile, opt-expected-move
• Where the spread is harvested/paid: strategy-iron-condor, strategy-strangle, strategy-straddle, mgmt-delta-hedging
• Regime context: regime-volatility