Greeks

What is Greeks?

Greeks The Greeks are risk measures that show how an option's price responds to changes in market variables. Named after the Greek letters used to represent them, they are the fundamental tools for understanding options risk and managing positions beyond beginner level. The five primary Greeks are delta, gamma, theta, vega, and rho. Each Greek measures sensitivity to a specific variable, holding everything else constant: - **Delta (Δ)**: How much the option price changes per $1 stock move. Range: 0 to +1 for calls, 0 to -1 for puts. - **Gamma (Γ)**: How much delta changes per $1 stock move (rate of change of delta). Always positive for long options. - **Theta (Θ)**: How much the option price changes per day of time passing. Negative for long options, positive for short options. - **Vega (ν)**: How much the option price changes per 1 percentage point change in implied volatility. Positive for long options. - **Rho (ρ)**: How much the option price changes per 1 percentage point change in interest rates. Typically the smallest Greek for short-dated options. Beyond the primary five, there are second-order Greeks (rate-of-change of the primary Greeks) and third-order Greeks used by sophisticated traders: - **Vanna**: Rate of change of delta with respect to IV. - **Charm**: Rate of change of delta with respect to time. - **Vomma (Volga)**: Rate of change of vega with respect to IV. - **Color**: Rate of change of gamma with respect to time. - **Speed**: Rate of change of gamma with respect to stock price. - **Zomma**: Rate of change of gamma with respect to IV. For individual options, the Greeks describe instantaneous sensitivity. For portfolios, Greeks aggregate linearly — sum the deltas of all positions to get net portfolio delta, sum the gammas for net gamma, etc. Position management at scale is fundamentally a Greek-aggregation exercise. Each strategy has a characteristic Greek profile that determines what helps and hurts the position: | Strategy | Delta | Theta | Vega | |----------|-------|-------|------| | Long call | + | - | + | | Long put | - | - | + | | Covered call | + | + | - | | Cash-secured put | + | + | - | | Iron condor | ~0 | + | - | | Long straddle | ~0 | - | + | Reading the Greeks of a position tells you immediately what market conditions you need for the position to print: directional move (delta), accelerating move (gamma), passage of time (theta), vol expansion or contraction (vega). Most options trading platforms display Greeks for every option chain entry. Aggregate position Greeks should always be checked before sizing a portfolio of options trades.