What is implied volatility and how does it relate to option price?

• A. Implied volatility is the volatility input that makes the Black-Scholes price equal to the observed market price; it represents market's expectation of future volatility.
• B. Implied volatility is the historical volatility observed in the past year.
• C. Implied volatility is the volatility input that represents the average volatility over the option's life.
• D. Implied volatility is the volatility input that makes the Black-Scholes price differ from the observed price.

Answer: (D)

Implied volatility is the volatility input in the Black-Scholes model that makes the model price match the observed market price of the option. It’s a forward-looking gauge, reflecting the market’s expectation of how much the underlying asset will move in the future, rather than the past realized moves. In practice, traders solve for this sigma by inverting the Black-Scholes formula given the option’s current price, the current underlying price, time to expiry, risk-free rate, and dividends. Because option prices rise with higher volatility, a higher implied volatility implies a more expensive option, and implied vol can differ across strikes and maturities, leading to features like the volatility smile or skew. The implied volatility is defined to align the model with the market price, not to create a price difference.