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The first-order greeks
Each greek answers one question: if a single input moves and everything else stays fixed, how much does the option's value change? Because they are partial derivatives of a pricing formula, they depend on the model chosen (Black-Scholes for European exercise, a binomial tree for American exercise), on the implied volatility fed into it and on the rate and dividend assumptions.
- Delta: change in option value per one-unit move in the underlying. Calls carry a delta between 0 and 1, puts between -1 and 0.
- Gamma: change in delta per one-unit move in the underlying. Long options have positive gamma, short options negative gamma.
- Vega: change in value per one-point change in implied volatility.
- Theta: change in value as one day passes, usually negative for a long option.
- Rho: change in value per one-point change in the risk-free rate.
Second-order greeks used in positioning work
Gamma exposure studies rely on cross-sensitivities as well. Vanna describes how delta changes when implied volatility changes; charm describes how delta decays as time passes. Both matter because a hedger who keeps a book delta-neutral has to adjust when volatility or the calendar moves, not only when spot moves. Near expiry these second-order terms can change quickly, which is why a greek printed at the open is stale by the afternoon.
Greeks versus exposure
A greek is a per-contract sensitivity. Exposure multiplies it by a position size, a contract multiplier and a sign that depends on who holds the position. Gamma exposure, vanna exposure and charm exposure are therefore one step further from the data than the greek itself: they add an assumption about dealer positioning that no exchange publishes. Keep the two layers apart when reading a dashboard.
In Senzoukria
The GEX module uses the greeks returned by the configured options provider, or computes them locally with Black-Scholes when the chain comes from Databento; without a chain the pages report that no option chain has come back rather than showing placeholder values. The Surface page offers a Value plotted selector with Gamma exposure, Vanna exposure, Charm exposure, Open interest and Implied volatility, and its note states that gamma, vanna and charm are model output while open interest and implied volatility come from the chain as published. The Calculation assumptions panel names the origin of the greeks, the provider or the local Black-Scholes (European) calculation, as a read-only value, and the regime panel shows a warning that vanna and charm rest on a stated percentage of the legs when only part of the chain returned.
Common mistakes
- Reading a greek as a market fact. It is a model value that changes with the volatility input and the exercise style selected.
- Comparing greeks from two providers without checking their model, rate and dividend settings.
- Treating a greek computed on yesterday's open interest as a description of today's positions.
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Frequently asked questions
- Which greek matters most for gamma exposure?
- Gamma is the direct input, since GEX scales gamma by position size and multiplier. Delta matters indirectly because gamma is the rate of change of delta, and vanna and charm matter when volatility or time is moving rather than spot. A GEX chart that ignores them is only a snapshot along the spot axis.
- Do greeks come from the exchange?
- No. Exchanges publish prices, volume and open interest. Greeks are computed by whoever runs a pricing model on that data, so the same chain can produce different greeks under different volatility, rate or exercise assumptions. A dashboard should say which model it used.
- Why do greeks change during the session even if nobody trades?
- Because spot, implied volatility and time to expiry all move. Gamma rises for at-the-money options as expiry approaches, delta drifts through charm and vanna, and a volatility shift reprices the whole surface. Open interest can stay fixed while every greek on the chain changes.