The Greeks
Delta, gamma, vega, theta, and rho translate model prices into hedge ratios, hedging costs, and the daily decay that funds them.
The Greeks are the partial derivatives of an option price with respect to its inputs, each one a sentence about hedging. Delta is the hedge ratio, the position in the underlying that makes a book locally immune to small moves; gamma measures how fast delta itself changes, so it is the cost of maintaining the hedge; vega and rho track sensitivity to volatility and rates; theta is the predictable daily decay that pays for the others. Because the sensitivities interact, desks manage them jointly, and large gamma or vega determines whether a book earns or bleeds. The Greeks turn Black–Scholes from a calculator into a risk-management system.