Meet the Greeks: Delta, Gamma, Theta, Vega, Rho
The greeks are how options react to changes in their inputs. One paragraph each on delta, gamma, theta, vega, and rho — plus how they combine in positions and why they matter most on 0DTE.
The greeks are how options react to changes in their inputs. Each greek measures one specific sensitivity — how the option's price will move when the underlying changes, when time passes, when implied volatility shifts, or when interest rates move. Learning to think in greeks is how you stop guessing what your option will do and start predicting it.
This article introduces the five main greeks in one place. Each one gets its own deep-dive article next in this module.
What greeks are
Mechanically, a greek is a partial derivative of the option's price with respect to one input. That sounds abstract; in plain English it means: if input X changes by a small amount, how much does the option's price change?
Greeks are computed values, not market quotes. They come from a model — usually Black-Scholes, covered in Black-Scholes in Plain English — so they're approximations of how the option will actually react. For typical conditions on longer-dated options, the approximations are very close to reality. For 0DTE in the final stretch, they're rougher.
Every modern options platform displays greeks alongside option prices. They aren't features of the option contract itself; they're features of how a model predicts the option will behave given the current inputs. When the inputs change — and they always do — the greeks themselves change too. They're a snapshot, not a constant.
Delta
The change in an option's price for a $1 change in the underlying. Ranges from 0 to 1 for calls, -1 to 0 for puts. Also approximately equals the probability the option finishes ITM.
A long call with delta 0.40 gains roughly $0.40 if the underlying rises by $1; a long put with delta -0.40 loses about $0.40 in the same scenario. Delta is also approximately the probability the option finishes ITM — a 30-delta call has roughly a 30% chance of expiring in-the-money. This dual interpretation (sensitivity and probability) makes delta the most-used greek in practice. Strategy descriptions like "short the 16-delta put" use it as a strike-selection criterion.
Full coverage: Delta.
Gamma
The change in delta for a $1 change in the underlying. The "acceleration" of delta. Always positive for long options, always negative for short options.
If a call has delta 0.40 and gamma 0.05, then after a $1 rise in the underlying its delta becomes approximately 0.45. Gamma matters because it tells you how unstable your delta is. Gamma is largest at ATM and especially near expiration — which is why 0DTE positions can re-price sharply for small underlying moves.
Long options always have positive gamma; short options have negative gamma. Sellers of premium are short gamma, which is the structural reason short-premium positions can move against you fast on small underlying moves.
Full coverage: Gamma.
Theta
The change in an option's price for one day of time passing, holding everything else constant. Long options have negative theta (they lose value over time). Short options have positive theta.
A long call with theta -0.10 loses about $0.10 of value per day if nothing else changes. Theta is the decay that premium sellers harvest. Theta is largest in absolute terms for ATM options near expiration — which is why most premium-selling strategies select near-ATM strikes on short-dated options.
For 0DTE, theta-per-day is an awkward measure since the contract has less than a day to live. Some platforms display per-hour or per-minute theta for short-dated options; others show daily theta that represents the entire remaining premium.
Full coverage: Theta.
Vega
The change in an option's price for a 1-point (1 percentage point) change in implied volatility. Long options have positive vega; short options have negative vega. Shrinks toward zero as expiration approaches.
A long call with vega 0.30 gains $0.30 if IV rises by 1 percentage point (say, from 15% to 16%). Vega is largest for long-dated options and at ATM. On 0DTE, vega in dollar terms is small — but a 1-point IV move can still meaningfully affect 0DTE option prices as a percentage of premium.
Vega is the one of the five that isn't actually a Greek letter despite the name.
Full coverage: Vega.
Rho
The change in an option's price for a 1-point change in the risk-free rate. Long calls have positive rho; long puts have negative rho. Smallest of the main greeks for short-dated options.
A long call with rho 0.05 gains $0.05 if the risk-free rate rises by 1 percentage point. For LEAPS (long-dated options) rho can matter materially; for 0DTE it's essentially zero. Most retail 0DTE traders don't track it.
Higher-order greeks, briefly
Beyond the five main greeks are second- and third-order sensitivities. The ones that show up most often in 0DTE discussions:
- Charm — how delta drifts over time, with everything else held constant. Significant near expiration: a position that's safely OTM at noon can have its delta drift toward zero (or toward one) purely from time passing.
- Vanna — how vega responds to underlying moves. Matters during volatility regime changes.
- Volga — how vega responds to vol moves. Largest for OTM options.
- Color, speed, zomma — third-order sensitivities; mostly relevant to professional market-making.
For retail 0DTE, charm is the second-order greek worth understanding. The others matter mostly to dealers managing complex books.
How greeks combine in a position
Different positions have different greek signatures. The four basic single-option positions:
| Position | Delta | Gamma | Theta | Vega |
|---|---|---|---|---|
| Long call | + | + | − | + |
| Long put | − | + | − | + |
| Short call | − | − | + | − |
| Short put | + | − | + | − |
A long call is +Δ +Γ −Θ +V — gains from underlying rallies, gets more bullish as the underlying rallies (positive gamma), loses value over time, gains from IV expansion. A short put has the same delta sign (positive, bullish) but the opposite gamma, theta, and vega signs.
For multi-leg positions, the greeks sum across legs. A short credit spread (short the higher-premium strike, long a further-OTM strike of the same type) has a small positive or negative delta depending on which side you're on, small negative gamma (the position is net short gamma), small positive theta (you collect more premium than you pay), and small negative vega.
Most multi-leg strategies are designed around producing a target greek profile. An iron condor is built to be approximately delta-neutral and short vega/gamma, generating theta over time. A long calendar spread is short the front month and long the back month at the same strike — typically long vega and positive theta. The position's behavior is determined by the greek totals, not by any one leg in isolation.
Why greeks matter especially on 0DTE
On 0DTE, greeks dominate position behavior more than they do on longer-dated trades:
- Gamma is enormous near ATM. Short ATM positions can lose hundreds of dollars per contract on small underlying moves.
- Theta IS the remaining premium. On a one-day option, theta-per-day equals the option's entire price.
- Vega is small in dollars but large in % terms. A 1-point IV change might move a $5 option by $0.10 — small in dollars, 2% of the option's price.
- Charm becomes meaningful. Delta drifts during the session even when the underlying doesn't move.
Without greek-thinking, 0DTE positions surprise you. Reading the greek snapshot on your chain — not just the price — is how you understand what a position is actually doing and what it will do if the underlying moves a particular way.
Key takeaways
- Greeks measure how an option's price will react to changes in each input — underlying, time, volatility, rates. They're computed from a model (usually BSM), not observed market quotes.
- The five main greeks: delta (sensitivity to underlying, ≈ ITM probability), gamma (delta's sensitivity to underlying), theta (time decay), vega (IV sensitivity), rho (rate sensitivity — mostly negligible for 0DTE).
- Multi-leg positions sum greeks. Most strategies are designed around producing a target greek profile (delta-neutral, theta-positive, etc.).
- Second-order greeks (charm, vanna, volga) become significant near expiration. Charm in particular matters for 0DTE.
- On 0DTE, greeks dominate behavior. Position outcomes are predicted by greeks more than by strike distance from spot.