Greeks
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Partial derivatives of option value: Δ = (partial V)/(partial S), Gamma = (partial^2 V)/(partial S^2), mathcalV(Vega) = (partial V)/(partial σ), Theta = (partial V)/(partial t), ρ = (partial V)/(partial r). Vega is not a Greek letter — an industry pseudo-Greek. Second-order cross-Greeks (Vanna = partial Δ / partial σ, Volga = partial^2 V / partial σ^2, Charm = partial Δ / partial t) drive volatility-surface risk management. The BSM PDE itself is a relation among Theta, Delta, and Gamma: Theta + r S Δ + 1/2σ^2 S^2 Gamma = r V.
Greeks in plain English
The Greeks are a set of 'dashboard gauges' for an option, each measuring how its price reacts to one thing changing while everything else holds still: Delta tracks moves in the stock, Gamma tracks how Delta itself shifts, Vega tracks changes in expected volatility, Theta tracks the ticking away of time, and Rho tracks interest rates. Traders watch them the way a pilot watches instruments — together they show every direction the option's value could get knocked around, so risk can be managed one lever at a time. (Fun fact: 'Vega' isn't actually a Greek letter — the industry just borrowed a name that sounds the part.) There are even second-level gauges like Vanna and Volga for the trickier interactions, but Delta, Gamma, and Theta are so linked that the famous option-pricing equation is really just a fixed relationship among those three.
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