Implied Volatility

The implied volatility (IV) of an option is the volatility level that, when plugged into the Black-Scholes model or other pricing formula, produces the option’s current market price. IV is not directly observable; it is derived by inverting the pricing formula. High IV means the market expects large price moves; low IV means the market expects calm. IV is the market’s consensus forecast of volatility over the option’s remaining life.

How implied volatility is derived

The Black-Scholes model price a call: C = f(S, K, T, r, σ)

The formula takes volatility σ as an input and outputs the fair call price C. When traders observe a market price in the exchange, they ask: what σ would make Black-Scholes produce this market price?

That σ is the implied volatility. There is no closed-form inverse; traders use numerical methods (Newton-Raphson iteration) to solve for IV.

IV as market expectation

Implied volatility is the market’s collective forecast. If a stock has 30-day implied volatility of 25%, the market is saying: “We expect this stock to move around 25% annualized over the next 30 days.” If IV is 50%, the market expects higher turbulence.

This is forward-looking, not backward-looking. Historical volatility measures realized moves over the past (e.g., 60 days). IV measures expected moves over the future. High IV does not mean the stock moved a lot; it means the market thinks it will.

IV across strikes: the volatility smile

In the real market, options at different strike prices have different implied volatilities. An at-the-money call struck at $100 on a $100 stock might have IV of 20%. An out-of-the-money put at $90 might have IV of 25%.

This variation across strikes is the volatility smile (U-shaped curve) or volatility skew (lopsided curve). It reflects the market’s fear of crashes (higher IV on OTM puts) and other skew effects.

IV across expirations: the term structure

IV also varies across expiration dates. Near-term options might have IV of 18%; one-year options might have 25%. This “volatility term structure” changes based on expected near-term events and long-term uncertainty.

Trading with implied volatility

IV rank and IV percentile: Traders compare current IV to historical IV levels. If IV is at the 90th percentile (highest in the past year), options are expensive; good time to sell. If IV is at the 10th percentile, options are cheap; good time to buy.

Mean reversion: IV tends to revert to long-term averages. Spikes in IV (panic selling, earnings surprises) are often temporary. Traders sell high IV and buy low IV, betting on reversion.

Volatility dispersion: Some traders buy options on individual stocks and sell index options (or vice versa), profiting if the correlation between individual stock and index volatility changes.

Vega and IV changes

The Greek vega measures sensitivity to IV changes. A long call with vega of +0.2 gains $0.20 if IV rises 1%. This makes vega directly relevant: if you believe IV is too low, you buy options (collect long vega) and profit when IV rises.

IV in exotics and path-dependent options

For exotic options (Asian, barrier, etc.), implied volatility is less directly used than for european-options, but the concept remains: IV embedded in exotic prices reflects market expectations of volatility over the option’s path.

See also