Delta is how much the option's price changes per $1 move in the underlying. Calls range 0 → +1, puts range −1 → 0. ATM ≈ ±0.50. As price moves, gamma causes delta to shift — giving options their convex payoff. Long options gain faster on winning moves and lose slower on losing moves.

Gamma is the rate at which delta changes per $1 move. Highest at ATM, near zero deep ITM/OTM. Explodes as expiration approaches — a small move near 0 DTE can flip delta dramatically. Long gamma: you benefit from large moves. Short gamma: you profit from stillness but bleed on big moves. See the Gamma Scenarios page for dealer flow detail.

Theta is the daily loss in option value due to time passing — all else equal. Long options lose theta every day. Short options collect theta. Decay is non-linear: accelerates sharply in the last 30–45 DTE. ATM options have the highest theta; deep ITM/OTM options have far less.

Vega is how much option value changes per 1% move in Implied Volatility (IV). Long options are long vega — you want IV to rise. Short options are short vega — you want IV to fall. IV crush after earnings can destroy long option value even if you predicted the direction correctly. Vega is highest ATM and declines for deep ITM/OTM options.

Vanna measures how delta changes when IV moves (equivalently, how vega changes when the underlying price moves). When IV rises, OTM options gain delta — they become more likely to expire ITM. When IV falls, that delta evaporates. Dealer vanna flows matter: dealers short OTM calls must buy more delta as IV rises (amplifying moves), and sell delta as IV falls. Vanna is largest for near-ATM, short-dated options.

Charm is the rate at which delta changes as time passes — think of it as "theta of delta." OTM option delta bleeds toward 0 every day (they become less likely to go ITM). ITM option delta firms toward 1 (binary outcome becomes clearer). ATM options stay near 0.50 but become explosively binary right at expiry. Dealers must rebalance hedges daily as charm shifts their delta exposure — creating systematic pressure.

Vomma (also called Volga) measures how vega itself changes as IV changes. High positive vomma means each additional % of IV rise makes the option more and more vega-sensitive — an accelerating effect. OTM options have high vomma: vega surges when vol spikes. ATM options have low vomma: vega changes nearly linearly. Long vomma positions (OTM options) are bets on vol-of-vol — that IV itself becomes more volatile. Short vomma (short OTM strangles) profit from vol stability but are exposed to vol acceleration.

Rho measures sensitivity to changes in the risk-free interest rate. Calls have positive rho — higher rates make calls slightly more valuable (cost-of-carry rises, owning the call is cheaper than owning stock). Puts have negative rho — higher rates make puts slightly less valuable. Rho matters most for long-dated LEAPS; for weekly options it is nearly negligible.

Speed is the 3rd order derivative of price with respect to underlying spot price ($\frac{\partial^3 V}{\partial S^3}$). It measures how fast gamma itself changes as the stock moves. Positive below ATM: gamma climbs as price rises toward strike. Negative above ATM: gamma decays as price pushes deeper ITM/OTM. Near 0 DTE, speed explodes into massive delta acceleration right around ATM strike pins.

Zomma measures how gamma changes when Implied Volatility (IV) moves (equivalently $\frac{\partial \text{Vanna}}{\partial S}$). Negative at ATM: when IV drops, gamma concentrates into an ultra-sharp needle; when IV rises, peak gamma drops. Positive on the wings: rising IV spreads gamma out into far OTM/ITM strikes.

Color measures the rate of change of Gamma over time ($\frac{\partial \text{Charm}}{\partial S}$). As expiration approaches, gamma at ATM strikes increases rapidly (positive Color), while gamma on outer wing strikes decays toward zero (negative Color). Color explains why 0 DTE options experience needle-like gamma spikes directly on the strike.

Ultima is the 3rd order derivative of price with respect to volatility ($\frac{\partial \text{Vomma}}{\partial \sigma}$). It measures the sensitivity of Vomma to changes in IV — the "vol-of-vol-of-vol". Ultima is critical for pricing deep out-of-the-money tail-risk hedges during extreme market stress and VIX explosions.

GEX (Gamma Exposure): Aggregate net dollar gamma held by market makers across strikes. +GEX (Above HVL / Gamma Flip): Dealers are long gamma → buy dips, sell rallies → volatility dampening / mean-reverting pin. −GEX (Below HVL / Gamma Flip): Dealers are short gamma → sell dips, buy rallies → volatility expansion / trend cascades. DEX & VEX: Net Delta positioning and Volume-weighted Greek exposure tracking real-time orderflow momentum.