The Greeks
Sensitivities of an option's price to each of its inputs. They are the vocabulary for describing what a position is actually exposed to.
MadStockAlerts Research · Updated August 29, 2026
What to take away
- Delta is sensitivity to the underlying price and is the largest exposure in most positions.
- Gamma is how fast delta changes, and it is what makes options non-linear.
- Theta is the decay of extrinsic value with the passage of time.
- Vega is sensitivity to implied volatility, which is a separate risk from direction.
- A position can be right about direction and lose on vega or theta.
MAD Academy Training Video · 0:46
Four Numbers That Explain the Move
Delta, gamma, theta and vega each measure sensitivity to one thing, and together they explain why a correct call still lost money.
This lesson is part of a Stock Alerts + Tools plan.
The five
| Greek | Measures | Sign for a long call |
|---|---|---|
| Delta | Change in premium per $1 move in the underlying | Positive, 0 to 1 |
| Gamma | Change in delta per $1 move | Positive |
| Theta | Change in premium per day of time passing | Negative |
| Vega | Change in premium per point of implied volatility | Positive |
| Rho | Change in premium per point of interest rate | Positive, usually small |
Delta is also frequently read as a rough approximation of the probability of finishing in the money, which is convenient and is not exactly what it measures.
Gamma is what makes an option an option
A position with a constant delta behaves like the underlying. Gamma is the rate at which delta changes as the underlying moves, and it is the source of the non-linearity that distinguishes an option from a stock position.
For a buyer, gamma is favourable: the position gains delta as it moves in their favour and loses it as it moves against, so gains accelerate and losses decelerate. For a seller it is the reverse, and the reversal is the central risk of selling options.
Gamma is largest at the money and rises sharply as expiry approaches. A short option that is near the strike close to expiry has a delta that can swing from near zero to near one within a session, which is why positions are frequently closed before that period rather than held into it.
Scroll the chart sideways to see all of it.
- 60 days to expiry
- 3 days to expiry
Theta and vega pull against each other
A long option loses value as time passes and gains value if implied volatility rises. A short option does the reverse. Most option positions are therefore a bet on the relationship between these two, whatever their directional appearance.
| Position | Theta | Vega | What it needs |
|---|---|---|---|
| Long option | Negative | Positive | Movement, soon, or rising implied volatility |
| Short option | Positive | Negative | Time to pass without a large move |
| Long calendar | Positive on balance | Positive | Time to pass and volatility to hold up |
| Long vertical | Reduced either way | Reduced either way | Direction, with less sensitivity to both |
The first row explains the most common disappointment for an option buyer. Being right about direction is not sufficient: the move has to be large enough and soon enough to overcome the decay, and implied volatility must not collapse in the meantime.
Reading a position through them
The Greeks are additive across positions, which is what makes them useful beyond a single contract. A portfolio's total delta describes its directional exposure regardless of how many contracts produced it.
- A total delta of 300 behaves approximately like 300 shares for small moves.
- A large negative gamma means that exposure worsens as the underlying moves in either direction.
- A large negative vega means a rise in implied volatility hurts, whatever the direction.
- A large positive theta means the position profits from time alone, and is usually paired with negative gamma.
The last combination is the profile that produces steady gains punctuated by severe losses, which is the pattern described in the risk-adjusted return article. The Greeks make that shape visible in advance rather than only in the returns.
Second-order effects
Beyond the five standard measures, a few second-order sensitivities describe how the first-order ones change. They matter mainly for positions held through large moves or across time.
| Measure | What it describes |
|---|---|
| Vanna | How delta changes as implied volatility changes |
| Charm | How delta changes as time passes |
| Vomma | How vega changes as implied volatility changes |
| Colour | How gamma changes as time passes |
Charm is the one with the clearest practical consequence for an ordinary position. An option's delta drifts toward zero or one as expiry approaches even with the underlying unchanged, so a hedge established on delta becomes wrong through the passage of time alone.
These are not measures anyone needs to compute to hold a position. They are named here because they explain why a position's behaviour changes without the underlying doing anything, which is otherwise puzzling.