European option greeks

Option Greeks quantify how an option’s price reacts to market variables. This visualization plots four key sensitivities for European call options across moneyness (the ratio of stock price to strike) and three maturities. Delta rises from near 0 out-of-the-money to near 1 in-the-money. Gamma, measuring delta curvature, peaks at-the-money where small price moves have the largest hedging impact. Vega, the sensitivity to volatility, also concentrates at-the-money. Theta captures time decay, strongest near the strike as expiration approaches. Color gradients show maturity effects: short-dated options display sharp, concentrated peaks, while longer-dated options have smoother profiles. 

Data: Theoretical Black–Scholes Greeks with strike K=100, risk-free rate r=3%, volatility σ=25%. Maturities: 0.1, 0.5, and 2.0 years. European call options only (no early exercise).