Implied Volatility
Definition
Implied Volatility (IV) is the volatility value that, when input into an option-pricing model (Black-Scholes), reproduces the option’s current market price. It is not a forecast — it extracts the market’s consensus view of future volatility from the price. “No trader knows the future, but in the option world people believe the option price contains the future.”
- Historical volatility looks backward — the volatility that has already happened.
- Implied volatility looks forward — the market’s current view of future volatility, expressed as an annualized figure so options can be compared.
Core Ideas
Computing historical volatility
- Logarithmic returns:
rₜ = ln(Pₜ / Pₜ₋₁) - Standard deviation of returns:
σ_daily = √( Σ(rₜ − r̄)² / (n−1) ) - Annualize:
σ_annual = σ_daily × √252(use √365 for crypto).
Extracting implied volatility
Black-Scholes for a call: C = S·N(d₁) − K·e^(−rT)·N(d₂). Every input except volatility is observable, so IV is found by numerical root-finding: guess σ, price the option, compare to market, adjust until model price matches market price. There is no closed-form solution.
Black-Scholes sensitivities (see Options Greeks): raising the underlying raises calls / lowers puts; raising the strike lowers calls / raises puts; less time lowers both; higher IV raises both calls and puts.
Moneyness and value
- ITM / ATM / OTM — in, at, or out of the money relative to spot.
- Intrinsic value — how far ITM the option is (only ITM options have it).
- Extrinsic value — option price minus intrinsic value; comes from time to expiry and uncertainty. Highest for ATM options, and grows with both time to expiry and IV.
Volatility smile
Black-Scholes assumes normally distributed returns, but real return tails are fatter — extreme moves happen more often. Traders price options near the extremes higher, producing a volatility smile (IV varies by strike, lowest near ATM). Variants: symmetrical smile, reverse skew/smirk (OTM puts richer), forward skew (OTM calls richer), and rarely a “frown.”
IV Rank — timing trades
IV Rank normalizes current IV against its 12-month range:
IV Rank = (Current IV − IV Low_12M) / (IV High_12M − IV Low_12M) × 100
- 0–25: IV is cheap; 50: mid-range; 75–100: IV is expensive.
Sell premium (e.g., Options Strategies like iron condors and strangles) when IV Rank is high to collect more; avoid selling when IV Rank is low.
Relationships
- Options Greeks — Vega measures sensitivity to IV
- Options Strategies — IV Rank drives premium-selling entry timing
- Trading & Finance — parent topic