How do option Greeks aggregate across a multi-leg position?

Greeks add linearly across positions: a portfolio's net delta is the sum of the deltas of its constituent options weighted by contract count. The same applies to gamma, theta, vega, rho, and the higher-order Greeks. This is why Greeks are operational: a position with +200 delta and +30 gamma describes a quantifiable risk profile that you can hedge by taking offsetting positions in the underlying or in offsetting options. Aggregate market-level Greeks (gamma exposure, dealer delta exposure) extend this to the whole options chain across all participants and reveal structural hedging pressure.

What's the relationship between vega and theta on a long option?

Vega and theta typically have opposite signs on long options: vega is positive (price rises with IV), theta is negative (price decays with time). Their relative magnitudes depend on tenor and moneyness. Long ATM options have the most vega in absolute terms and the most theta; they're most sensitive to both IV moves and time decay. As expiration approaches, theta accelerates and vega contracts; the relative weight shifts heavily toward theta in the final two weeks. This is why short-dated long options are 'theta plays'; vega has limited room to help.

How accurate are option Greeks at expiration?

Greeks degrade in reliability as expiration approaches because the option's price function becomes discontinuous at the strike at expiration. Gamma spikes near ATM in the final week (sometimes called 'pin gamma'), making delta extremely sensitive to small price changes. Theta accelerates non-linearly. Standard analytical Greeks are technically correct but mislead practical risk management; a position with +50 delta on Friday morning can flip to 0 or 100 by Friday afternoon as spot moves through the strike. For final-week trading, consult both the analytical Greeks and the realized P/L distribution under multiple spot scenarios.

How do you read a Greek decomposition for a multi-leg position?

Greek decomposition lists the contribution of each leg to the position's net Greeks. For an iron condor: the short-call leg contributes negative delta and negative gamma; the long-call wing offsets some gamma but adds vega; the short-put leg contributes positive delta and negative gamma; the long-put wing offsets puts gamma. Reading the decomposition reveals which legs dominate which risks: typically the short legs dominate gamma and theta, the long wings dominate vega in the wings. The platform exposes Greek decomposition on every multi-leg structure in the strategy builder.

What is gamma exposure (GEX) and why does it matter?

Gamma exposure aggregates per-strike gamma across the whole options chain, weighted by open interest and signed by who holds each side. Positive aggregate GEX means dealers are net long gamma: they hedge by selling rallies and buying dips, dampening volatility. Negative GEX means dealers are net short gamma: they hedge by selling dips and buying rallies, amplifying volatility. The GEX flip level (where aggregate GEX crosses zero) is often a regime boundary that materially changes intraday price behavior. Per-ticker GEX views surface these levels with strike-level resolution.

The 17 Greeks: Complete Deep-Dive Reference

Last reviewed: May 17, 2026 by Options Analysis Suite Research.

Greeks are the partial derivatives of option value with respect to its inputs. They are the operational language of options risk management: each Greek isolates one source of price sensitivity (spot, time, volatility, rates, dividends) so a position can be measured and hedged against that single dimension. We compute all 17 industry-standard Greeks plus the Heston-specific parameter sensitivities; each link below opens a deep-dive page covering formula, intuition, worked example, how each pricing model computes it, operational use, and references.

What Are the Standard 17 Greeks?

Delta (Δ) - Delta is the first derivative of option value with respect to the underlying price; it equals N(d1) for calls and N(d1)-1 for puts in Black-Scholes, and is the central hedge ratio used to translate between stock and option exposure.
Gamma (Γ) - Gamma is the second derivative of option value with respect to the underlying price (and equivalently the rate of change of delta); it equals phi(d1) / (S sigma sqrt(T)) in Black-Scholes and drives the convexity of an option position.
Theta (Θ) - Theta is the first derivative of option value with respect to time-to-expiration; it captures the rate at which an option loses value as expiration approaches and is structurally negative for long options.
Vega (ν) - Vega is the first derivative of option value with respect to implied volatility; it equals S phi(d1) sqrt(T) in Black-Scholes and is the sensitivity used to translate IV moves into dollar P&L on an options position.
Rho (ρ) - Rho is the first derivative of option value with respect to the risk-free interest rate; it equals K T exp(-rT) N(d2) for calls in Black-Scholes and is the sensitivity that dominates risk for long-dated options and warrants.
Vanna - Vanna is the cross-derivative of option value with respect to spot and volatility; equivalently, it measures how delta changes when IV changes, or how vega changes when spot moves.
Charm - Charm is the cross-derivative of option value with respect to spot and time-to-expiration; equivalently, it measures how delta decays as expiration approaches, and it dominates dealer end-of-day rebalancing especially in the closing hour and at weekends.
Vomma - Vomma (also called Volga or vega convexity) is the second derivative of option value with respect to volatility; equivalently, it measures how vega itself changes with IV, and it is the structural exposure traded by butterflies and other vol-of-vol structures.
Speed - Speed is the third derivative of option value with respect to the underlying price; equivalently, it measures how gamma itself changes as spot moves, and it captures the convexity of convexity that becomes important in large moves and near expiration.
Zomma - Zomma is the third-order cross-derivative of option value with respect to spot (twice) and volatility; equivalently, it measures how gamma itself changes when IV changes, and it captures gamma-stability across volatility regimes.
Color - Color (also called gamma decay or DgammaDtime) is the third-order cross-derivative of option value with respect to spot (twice) and time; it measures how gamma itself decays toward expiration and is critical for understanding expiration-week dealer flow.
Veta - Veta (also called DvegaDtime) is the second-order cross-derivative of option value with respect to volatility and time; it measures how vega itself decays as expiration approaches and is the structural exposure traded by calendar spreads.
Ultima - Ultima is the third derivative of option value with respect to volatility; equivalently, it measures how vomma itself changes with IV, and it captures the convexity of vega convexity that matters in extreme vol regimes.
Lambda (λ) - Lambda (also called Omega or elasticity) is the percentage change in option value per percentage change in underlying price; it equals delta times (S/V) and is the structural leverage measure for sizing positions and comparing capital efficiency.
Epsilon (ε) - Epsilon (sometimes Psi) is the first derivative of option value with respect to dividend yield; it equals -S T exp(-qT) N(d1) for calls under continuous-dividend Black-Scholes and is the structural sensitivity for index and high-yield equity options.
Phi (Φ) - Phi is the first derivative of option value with respect to the foreign risk-free rate; it appears in the Garman-Kohlhagen FX-options model alongside the standard rho (domestic-rate sensitivity) and is the structural sensitivity for currency-options carry trades.
DcharmDvol - DcharmDvol is the third-order cross-derivative of option value with respect to spot, time, and volatility; equivalently, it measures how charm (delta-decay) changes when IV changes, and it appears in advanced multi-dimensional hedging analytics.

What Are the Heston-Specific Greeks?

When an option is priced under the Heston stochastic-volatility model, additional sensitivities become available beyond the standard 17 Greeks.

RhoR (ρ_r) - RhoR is the first derivative of option value with respect to the risk-free interest rate, computed under the Heston stochastic-volatility model.
RhoQ (ρ_q) - RhoQ is the first derivative of option value with respect to the dividend yield, computed under the Heston stochastic-volatility model.
Epsilon2 (ε₂) - Epsilon2 is the second derivative of option value with respect to dividend yield (the convexity of value in dividend space).
Kappa Der (κ) - Kappa Der is the first derivative of option value with respect to the Heston mean-reversion speed parameter (kappa).
Theta Param (θ) - Theta Param is the first derivative of option value with respect to the Heston long-run variance parameter (theta).
Vol of Vol (ν) - The Vol of Vol Greek (often called nu sensitivity or xi sensitivity) is the first derivative of option value with respect to the Heston vol-of-vol parameter.
Rho Der (ρ) - Rho Der is the first derivative of option value with respect to the Heston spot-vol correlation parameter (rho).

How Do Traders Use the Greeks?

Greeks are the operational language of options risk management. Delta sizes directional exposure and tells you how many shares of underlying an option position behaves like. Gamma measures how that delta changes with spot, so it dictates rebalancing frequency for delta-hedged books. Theta is the daily premium decay every long option pays for time. Vega is the dollar P&L per 1% change in implied volatility, which is what drives long-vol versus short-vol trades. Higher-order Greeks (vanna, charm, vomma, speed) become operationally relevant for dealer hedging desks managing large option inventories, where second- and third-order sensitivities drive flow that shows up in observable market microstructure.

Calculate any Greek for any option in our free Research Terminal - no account required. Live aggregate dealer Greeks (gamma, delta, vanna, charm, vomma) are visible in the SPY GEX dashboard.

Related Reference

For the full pricing-model reference set, see the Pricing Model Landscape. For the retail-vocabulary entry points that bridge to these Greeks, see the concept pages: Dealer Gamma, Gamma Squeeze, 0DTE Options, Leverage Effect, Vol of Vol, IV Crush.