What implied volatility tells you — the market's expectation of future price movement

What volatility smile shows — implied volatility varies with strike price, contradicting Black-Scholes

Volatility smile indicates implied volatility's non-linearity with respect to strike prices

How do implied volatility, beta, and alpha influence the pricing and risk management of equity options?

Implied volatility, beta, and alpha affect option pricing and risk management by indicating market sentiment, systemic risk, and stock performance respectively

How does implied volatility decay affect the pricing of exotic options, particularly as the expiration date approaches?

Implied volatility decay increases the value of long-dated exotic options as expiration nears

What vega measures — an option's sensitivity to a 1% change in implied volatility

Vega measures an option's price change per 1% implied volatility adjustment

What delta measures in the context of options trading, and how does it relate to the price change of an option for a 1-point movement in the underlying asset's price?

Delta measures an option's sensitivity to underlying asset price changes, typically 0.25 for a $1 move

What the Black-Scholes formula prices — European call and put options

Black-Scholes prices European call and put options using volatility, interest rates, and time to expiration