Black-Scholes Model

The Black-Scholes Model, developed by Fischer Black, Myron Scholes, and Robert Merton in 1973, is the foundational mathematical framework for pricing European-style options — options that can only be exercised at expiry. The model calculates the theoretical fair value of a call or put option based on five inputs: the current price of the underlying asset, the option's strike price, the time to expiry, the risk-free interest rate, and the volatility of the underlying asset. The model assumes continuous trading, constant volatility, no dividends, no transaction costs, and normally distributed returns — assumptions that are simplifications of real-world market behaviour. Despite these limitations, the Black-Scholes Model revolutionised options trading and risk management and remains the standard reference framework for option pricing globally. In Indian F&O markets, the Black-Scholes formula is used to calculate the theoretical prices of Nifty 50 and Bank Nifty options, derive implied volatility from observed market prices, and compute the options Greeks (Delta, Gamma, Theta, Vega, Rho) that measure option price sensitivity to each input. Myron Scholes and Robert Merton were awarded the Nobel Prize in Economics in 1997 for their contribution to this model.