Implied Volatility (IV)

The volatility that, when input into the BSM model, makes the model price equal to the market price of an option.

Implied volatility is 'backed out' of the market option price by solving BSM in reverse. Since BSM has no closed-form inverse for sigma, it is solved numerically — typically using Newton-Raphson iteration: σ_{n+1} = σ_n − [BSM(σ_n) − Market Price] / Vega(σ_n), converging in 5–10 iterations. IV represents the market's consensus forecast of future realized volatility for the underlying. When IV > realized vol, options are 'overpriced'. IV smile/skew patterns reveal market risk aversion and demand for out-of-the-money protection.

Related Terms

Black-Scholes-Merton Model (BSM)

The foundational option pricing formula that gives the fair value of a European call or put as a function of spot, strike, rate, volatility, and time.

Vega (ν)

The sensitivity of an option's price to a 1% change in implied volatility.

Historical Volatility (HV)

The realized standard deviation of the asset's returns over a historical lookback window, typically annualized.

Volatility Smile

The pattern where implied volatility is higher for deep in-the-money and out-of-the-money options than for ATM options.