Implied Volatility vs Volatility Smile

The annualized standard deviation of price returns implied by the current market price of an option, derived by solving the Black-Scholes model backwards from observed market price; forward-looking measure of expected future volatility; distinct from historical volatility which measures past realized movement.

The pattern that emerges when implied volatility is plotted across option strikes for the same expiry; deviates from the flat IV assumed by Black-Scholes; in crypto markets, both OTM calls and OTM puts often carry higher IV than ATM options, reflecting two-sided tail risk expectations.