For an engineer, an option's price is a function of state variables and the Greeks are just its partial derivatives — Delta is dV/dS, Gamma is the second derivative, Theta is dV/dt, Vega is sensitivity to volatility, Rho to interest rates. This post demystifies the Greeks for a technical audience: the Black-Scholes pricing function and its closed-form Greeks in Python with scipy, the intuition behind each sensitivity, delta-hedging as a feedback control loop, the gamma-theta tradeoff that is the real engine of options P&L, portfolio-level risk aggregation, and an honest accounting of where the model's assumptions break (constant volatility, no jumps, the volatility smile).
Options
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The Engineering of Options Trading: The Greeks as Partial Derivatives