The Black-Scholes model is a mathematical formula developed in 1973 by Fischer Black, Myron Scholes, and Robert Merton to calculate the theoretical price of European-style options. It considers several factors: the underlying asset's price, the strike price, time until expiration, risk-free interest rates, and volatility. The model assumes markets are efficient, with no arbitrage opportunities, and that asset prices follow a log-normal distribution. While widely used, it has limitations, such as ignoring dividends and assuming constant volatility, an assumption often contradicted in real markets.

Implied volatility (IV) is derived by reversing the Black-Scholes model: instead of inputting volatility to get an option’s price, traders input the market price of an option to solve for volatility. This backwards calculation reveals the market’s expectation of future price fluctuations. When IV rises, option premiums become more expensive due to higher uncertainty, and vice versa. The Black-Scholes model thus serves as the foundation for quantifying IV, helping traders assess whether options are overpriced or underpriced relative to historical volatility. Despite its simplifications, the model remains a cornerstone in options pricing, with implied volatility being a critical metric for strategies like straddles, volatility arbitrage, and risk management.