A single option has a delta, a gamma, a theta and a vega. A position with three legs has three of each, and nobody can watch twelve numbers at once. The fix is simple: Greeks add. Add up each Greek across the legs and the whole position collapses to one delta, one gamma, one theta and one vega. Those four numbers tell you what the position does when the stock moves, when it keeps moving, when a day passes, and when the market's estimate of future movement, the implied volatility, changes.
The sign comes from the side
The chain lists Greeks for a long option, one you own. When you sell an option, every Greek flips sign. A long call with a delta of 0.53 becomes a delta of minus 0.53 if you sold it. The same rule applies to gamma, theta and vega, and it applies before you add anything. So the recipe is: take each leg's Greeks from the chain, flip the sign for any leg you sold, multiply by the number of contracts, then add the legs together.
A straddle, added up
Say a stock is at $200 and the 30-day at-the-money options, priced at 35% implied volatility, look like this, per share:
| Leg | Delta | Gamma | Theta | Vega |
|---|---|---|---|---|
| Buy $200 call | 0.53 | 0.020 | -0.14 | 0.23 |
| Buy $200 put | -0.47 | 0.020 | -0.12 | 0.23 |
| Long straddle | 0.06 | 0.040 | -0.26 | 0.46 |
These are textbook figures, which give the call a slightly larger theta than the put. The Terminal's chain shows one theta per strike for both sides, about minus 0.13 here, as the Theta lesson explained; doubled, it lands on almost the same total.
The call's positive delta and the put's negative delta almost cancel, so the straddle barely cares which way the stock moves next. What is left is everything else, doubled: gamma of 0.040, so the delta builds quickly in whichever direction the stock goes; theta of minus 0.26, so the position gives up 26 cents a share every day the stock sits still; and vega of 0.46, so a 1-point rise in implied volatility adds 46 cents a share. Per contract, multiply by 100: the straddle costs about $1,600, loses about $26 a day and gains about $46 for every vol point.
Sell the same straddle and every number flips. Delta is still near zero, but gamma is minus 0.040, theta is plus 0.26 and vega is minus 0.46. The seller earns $26 a day and is hurt by a big move in either direction or by a rise in implied volatility. Same two options, opposite risk.
Net Greeks change shape as the stock moves
The table is a snapshot at $200. Move the stock and each leg's Greeks change, so the net numbers change too. The chart below plots the net Greeks of a short straddle on a $100 stock against the stock price. Switch between the four Greeks and watch the shapes: gamma and vega are deepest right at the strike, where the seller is most exposed, and fade as the stock runs away in either direction.
Sell the $100 call and the $100 put, with 30 and 7 days left. Switch between the Greeks: gamma, vega and theta peak at the strike, and delta tilts against you whichever way the stock goes. Raise volatility to see the shapes spread out.
Delta is the one to study. At the strike it is near zero, which is why a short straddle looks harmless on the morning you sell it. A few dollars away it is no longer zero: the seller is short the stock as it rallies and long the stock as it falls, always on the wrong side of the move. That drift is the net gamma at work, and it gets steeper as expiry approaches.
An iron condor: four legs, one row
An iron condor sells a put and a call out of the money and buys a put and a call further out to cap the loss. On a $100 stock: sell the 95 put, buy the 90 put, sell the 105 call, buy the 110 call. Four legs, sixteen Greeks, and they still collapse to one row. With 45 days left at 30% volatility, the net is delta close to zero, gamma about minus 0.019, theta about plus 0.023 and vega about minus 0.071 per share. It is a smaller, fenced-in version of the short straddle.
Short the 95 put and 105 call, long the 90 put and 110 call. Start on gamma: negative between the short strikes, positive out past the long ones, and far sharper with 3 days left. Switch to delta and vega to see the same flip.
The shape is where it gets interesting. Between the short strikes the condor is short gamma, like the straddle. Out past the long strikes the bought options take over and net gamma turns positive. So the same position is short gamma if the stock sits still and long gamma if it has already run through a wing. Its net Greeks at one price say nothing about its net Greeks $8 away, and the gap widens as expiry nears. That is why a desk reads the whole curve, not one row.
Why the net numbers matter
Once a position is reduced to four net Greeks you can compare positions that look nothing alike. A short straddle and a short iron condor are both short gamma and short vega with positive theta; they differ in how much. A long call and a long put are both long gamma; a straddle is just both at once. Every position-level question in this module, how much a scenario costs, how much a hedge fixes, starts from the net Greeks.
The maths: why Greeks add, and what does not
A position's value is the sum of its legs: V = Σ wᵢ Cᵢ, where Cᵢ is leg i's price per share and wᵢ is its signed quantity (+1 bought, -1 sold, times the number of contracts). A Greek is a derivative, and the derivative of a sum is the sum of the derivatives, so Δ_V = Σ wᵢ Δᵢ, Γ_V = Σ wᵢ Γᵢ, and the same for theta and vega. That is exact, not an approximation, as long as every leg is measured at the same stock price, time and volatility.
The iron condor above, leg by leg at 45 days and 30% vol (per share, sign already applied):
| Leg | Delta | Gamma | Theta | Vega |
|---|---|---|---|---|
| Sell 95 put | 0.279 | -0.032 | 0.036 | -0.118 |
| Buy 90 put | -0.136 | 0.021 | -0.024 | 0.077 |
| Sell 105 call | -0.358 | -0.035 | 0.047 | -0.131 |
| Buy 110 call | 0.210 | 0.027 | -0.036 | 0.101 |
| Net | -0.005 | -0.019 | 0.023 | -0.071 |
Check the delta column: 0.279 - 0.136 - 0.358 + 0.210 = -0.005. What does not add so simply is P&L over a real move. The Greeks are slopes at one point, and a position's value is curved, so the P&L of a $10 move is not ten times the P&L of a $1 move. The next lesson puts numbers on that.
Your turn
Open Strategy Lab on NVDA, build the at-the-money straddle on the monthly expiration, and read the net Greeks off the NET row. Then do one by hand on the SPY chain, adding the call's theta to the put's, so you know what the panel saved you.