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Options Greeks & dealer positioning, explained
Every Greek a trader runs into, first order to third, in plain English: what it measures, the Black-Scholes formula, how it moves, and what it means when market makers hold it in size. Written by the people who build Zanshin Flow, with the numbers from our own archive where we've tested a claim. Educational content only; not financial advice.
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First-order Greeks
- First-order Greek · ∂V/∂SDelta: how much an option moves with the underlyingOption delta explained: the Black-Scholes formula, why calls run 0 to 1 and puts 0 to −1, delta as a hedge ratio, and dealer delta exposure (DEX).
- First-order Greek · ∂V/∂tTheta: what time costs an optionOption theta explained: the Black-Scholes time-decay formula, why decay accelerates near expiry, the theta-gamma trade-off, and dealer theta exposure.
- First-order Greek · ∂V/∂σVega: what a point of implied volatility is worthOption vega explained: the Black-Scholes formula, why long-dated at-the-money options carry the most, vega vs gamma, and dealer vega exposure.
- First-order Greek · ∂V/∂rRho: an option's sensitivity to interest ratesOption rho explained: the Black-Scholes formula, why calls have positive rho and puts negative, and why rho barely matters for short-dated options.
Second-order Greeks
- Second-order Greek · ∂²V/∂S²Gamma: how fast delta changesOption gamma explained: the Black-Scholes formula, why it peaks at the money and explodes near expiry, long vs short gamma, and what dealer gamma does to price.
- Second-order Greek · ∂²V/∂S∂σVanna: how delta changes when implied volatility movesVanna explained: the Black-Scholes formula, its sign above and below the strike, vanna hedging flows when IV falls, and what we found testing them.
- Second-order Greek · ∂²V/∂S∂tCharm: how delta decays as time passesCharm (delta decay) explained: the formula, why it's huge for same-day options, how time decay turns into dealer hedging flow, and the charm surface.
- Second-order Greek · ∂²V/∂σ²Vomma (volga): the convexity of an option to implied volatilityVomma, also called volga or vega convexity, explained: the Black-Scholes formula, why out-of-the-money wings carry it, and why it prices the smile.
Third-order Greeks
- Third-order Greek · ∂³V/∂S³Speed: how fast gamma changes as price movesThe speed Greek explained: the third derivative of option value to price, its Black-Scholes formula, what it says about a gamma book, and our test of it.
- Third-order Greek · ∂³V/∂S²∂tColor: how gamma changes as time passesThe color Greek (gamma decay) explained: its formula, why at-the-money gamma grows into expiry while far strikes fade, and what it means for 0DTE.
- Third-order Greek · ∂³V/∂S²∂σZomma: how gamma changes when implied volatility movesThe zomma Greek explained: the Black-Scholes formula, why higher implied vol flattens the gamma profile, and what it means for dealer gamma maps.
- Third-order Greek · ∂³V/∂σ³Ultima: the third derivative of an option to implied volatilityThe ultima Greek explained: its Black-Scholes formula, how it relates to vega and vomma, and when a volatility trader would ever look at it.
Dealer positioning
- Dealer positioningGamma exposure (GEX): the dealer gamma book, in dollarsWhat gamma exposure (GEX) is, how it's calculated per strike, why positive GEX dampens moves and negative GEX amplifies them, and the assumptions behind it.
- Dealer positioningThe gamma flip: where dealer gamma changes signThe gamma flip, or zero-gamma level, explained: how it's computed by repricing the dealer book, what changes above and below it, and what our data says.
- Dealer positioningWhat is a call wall and a put wall in options trading?A call wall is the strike with the most call gamma; a put wall, the most put gamma. What they mean, when a put wall is support or a trapdoor, and how often they held.
- Dealer positioningDealer hedging: how market makers turn options into flowHow options market makers delta-hedge, why gamma, charm and vanna force them to keep trading, and how hedging flow is estimated from the options tape.
- Dealer positioning0DTE options: why same-day expiries dominate intraday flowWhat 0DTE (zero days to expiration) options are, why their gamma and charm are so large, how dealers hedge them, and how to read a 0DTE gamma map.
- VolatilityImplied volatility skew: why puts cost more than callsWhat implied volatility skew and the volatility smile are, why index puts trade at higher IV than calls, risk reversals, and how to read skew changes intraday.
- VolatilityExpected move: the range options are pricingHow to calculate an expected move from implied volatility, what 1σ and 2σ mean, and how well same-day implied moves matched reality in our data.