The Greeks (Option Greeks)

The Greeks, or option Greeks, are sensitivity metrics used in option pricing and risk management. They quantify how an option's price responds to changes in the key input parameters. Delta measures the sensitivity to the underlying asset price, Gamma is the sensitivity of Delta itself, Theta captures time decay, Vega measures sensitivity to volatility, and Rho captures sensitivity to interest rates. Together, they enable hedging and risk assessment. Core principles: 1) Delta = ∂C/∂S; 2) Gamma = ∂^2C/∂S^2; 3) Theta = ∂C/∂t; 4) Vega = ∂C/∂σ; 5) Rho = ∂C/∂r. In practice, these are derived from pricing models (most commonly Black–Scholes) and are used to manage directional risk, curvature, time decay, volatility exposure, and interest-rate exposure. Commonly, for calls, Delta ∈ [0,1], and for puts, Delta ∈ [−1,0]. However, actual values depend on moneyness, time to expiry, and market conditions. While the Greeks are powerful, they assume model parameters are stable; real markets exhibit jumps and stochastic volatility, which can reduce hedging effectiveness. Additional Greeks (Charm, Vanna, Vomma, Color) extend coverage of dynamic risk across time and volatility.