): The time remaining until the option expires, usually expressed in years. Risk-Free Interest Rate (
The Black-Scholes model, also known as the , is a mathematical framework used to determine the fair price or theoretical value of an options contract. Introduced in 1973, it revolutionized modern finance by providing a structured way to manage risk and value complex derivatives. The Core Formula and Variables black scholes model
): The theoretical rate of return on an investment with zero risk, such as a government bond. Volatility ( ): The time remaining until the option expires,
represent the cumulative standard normal distribution, calculating the probability that the option will expire in-the-money. Key Assumptions also known as the