Mastering Python for Finance - Second Edition

The implied volatility model

Perhaps one of the most widely-studied option-pricing models is the Black-Scholes-Merton model, or simply the Black-Scholes model. A call option is a right, but not an obligation, to buy the underlying security at a particular price and time. A put option is a right, but not an obligation, to sell the underlying security at a particular price and time. The Black-Scholes model helps determine the fair price of an option with the assumption that the returns of the underlying security are normally distributed (N(.)) or that asset prices are log-normally distributed.

The formula takes on the following assumed variables—the strike price (K), the time to expiry (T), the risk-free rate (r), the volatility of the underlying ...