Implied volatility

Definition

Implied volatility (IV) is the volatility number that makes an option-pricing model’s output equal the option’s market price — the market’s priced expectation of the underlying’s future movement over the option’s life, expressed as an annualized standard deviation. IV is quoted per contract; a whole chain’s IVs form the volatility surface.

How it works / structure

• Computation: invert the pricing model (Black-Scholes-class) numerically: given price, S, K, T, r, dividends, solve for σ. There is no closed form; root-finding on the model price.
• Conventions: annualized percentage (IV 30 = 30% annualized); converting to horizon moves uses σ·√(T) scaling (opt-expected-move).
• Index construction: the Cboe VIX methodology computes a 30-day model-free IV for the S&P 500 from a strip of option prices — the standard volatility-regime marker (regime-volatility).
• Platform bindings: iv_rv_ratio (IV vs realized), implied_earnings_move_pct and earnings_iv_crush_pts (event IV mechanics, event-earnings).
• Simulation parameters: entry/exit IV per leg, IV paths for repricing, and event-crush modeling for positions spanning earnings.

When it applies

Everywhere in options analysis: comparing option richness across strikes/expiries/underlyings (raw premium is incomparable; IV is the normalizer), volatility theses (IV vs subsequent realized), event pricing, and strategy selection (premium-selling entries key on high IV vs history — opt-iv-rank-percentile).

Risk profile & failure modes

• Model-dependence: IV is defined through a model; American exercise, dividends, and rate assumptions shift the number — cross-vendor IVs disagree on the same contract.
• Thin-quote garbage: IV from stale or wide quotes is noise (ms-option-chain liquidity filters come first).
• Expectation ≠ forecast: IV embeds a risk premium; reading it as an unbiased forecast of realized volatility systematically overstates future movement (see evidence below).
• Surface collapse to one number: quoting “the IV” of an underlying hides skew and term structure that carry the thesis- relevant information.

Evidence & limits

Christensen and Prabhala (1998) found IV predicts subsequent realized volatility and subsumes much of history’s information — IV is informative. Bakshi and Kapadia (2003) documented negative delta-hedged gains consistent with a negative volatility risk premium: index IV on average exceeds subsequent realized volatility, i.e. options are on average priced rich as insurance. That premium is time-varying and reverses in stress — “IV is always overpriced” is folklore; the measured statement is the average premium with crisis exceptions.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X’s 30-day IV, at 45 today, will exceed the volatility realized over the same 30 days” — falsified by realized volatility ≥ 45.
• “Y’s front-month IV will drop at least 8 points the session after earnings” — falsified by the post-report IV print.

Cross-references

• Normalizations: opt-iv-rank-percentile; surface: opt-volatility-skew, opt-term-structure
• Derived expectation: opt-expected-move
• Exposure to it: greek-vega; realized comparison: indicator-realized-vs-implied-vol
• Regime marker: regime-volatility; event mechanics: event-earnings