Lesson 1 described what a premium seller is paid for. This lesson describes how that payment arrives and what can take it away. The four Greeks are introduced in the Learn article on options Greeks; here we look at them strictly from the seller's side and use them to answer three practical questions: how far out to sell, how far from the price to sell, and when to get out.
All numbers below come from the Black–Scholes model with the stock at 100, 30% implied volatility, no dividends and no interest rate. Real chains differ because of skew and dividends, but the shapes are the same.
Theta: how the premium is earned
An option's price above its intrinsic value is time value. If nothing else changes, time value falls to zero by expiry, and that decay is the seller's income. Theta measures it per day. For a short option, Theta is positive: the position gains value as the clock runs.
Decay is not linear. For an at-the-money option, time value is roughly proportional to the square root of the time left, so it falls slowly at first and quickly at the end:
| Days to expiry | At-the-money value | Theta per day | Gamma | Vega per IV point |
|---|---|---|---|---|
| 45 | $4.20 | $0.047 | 0.038 | $0.140 |
| 21 | $2.87 | $0.069 | 0.055 | $0.096 |
| 7 | $1.66 | $0.123 | 0.096 | $0.055 |
The last three weeks look like the most profitable time to be short, since Theta is highest. The table shows the catch: Gamma rises just as fast. Theta and Gamma are two sides of the same coin. A seller earns Theta precisely because they accept Gamma risk, and near expiry both are large.
Out-of-the-money options decay differently. Their time value is smaller in dollars and erodes more evenly; a far out-of-the-money option can lose most of its value well before the final week. This is one reason sellers of 15–30 delta options often reach half their maximum profit well before expiry.
Delta: direction and a rough probability
A short put has positive Delta (you gain when the stock rises); a short call has negative Delta. Because a contract covers 100 shares, a short put with Delta −0.30 behaves like owning 30 shares. Add the Deltas of all legs to see the position's net exposure in share terms.
Traders also use Delta as a quick estimate of the chance an option finishes in the money. In the model, the estimate is close but not exact: for puts the true model probability is slightly higher than |Delta|, for calls slightly lower. The chance of the price touching a strike at some point before expiry is roughly twice its Delta, which matters to anyone who manages trades when the strike is tested.
| Option, 35 days | Price | Delta | Model chance in the money | Rough chance of touch |
|---|---|---|---|---|
| 95 put | $1.65 | −0.28 | 31% | about 55% |
| 92 put | $0.90 | −0.17 | 20% | about 35% |
| 90 put | $0.56 | −0.12 | 14% | about 24% |
| 105 call | $1.81 | 0.32 | 28% | about 63% |
| 108 call | $1.10 | 0.22 | 19% | about 43% |
The table makes the trade-off concrete. Moving from the 95 put to the 90 put cuts the chance of finishing in the money by more than half, and the premium by two-thirds. There is no free lunch in strike selection: probability and payment move together.
Gamma: the risk that grows near expiry
Gamma is the rate at which Delta changes as the stock moves. Short options have negative Gamma: as the stock moves against you, your exposure grows in the wrong direction. A short put that started at −0.30 Delta can reach −0.60 after a sharp drop, so each further dollar of decline costs twice as much as the first.
The effect on a short at-the-money put when the stock falls $3 in one day:
- With 45 days left, the put rises from $4.20 to about $5.77: a loss of $1.57, or 37% of the premium collected.
- With 7 days left, it rises from $1.66 to about $3.46: a loss of $1.80, more than the entire premium.
That asymmetry is why many sellers avoid holding short options through the last two or three weeks, even though Theta is at its highest there.
Vega: exposure to implied volatility
Short options have negative Vega: they lose when implied volatility rises. The 35-day 95 put above has a Vega of about $0.10 per IV point. If IV rises from 30% to 35% with the stock unchanged, the put goes from $1.65 to about $2.18, a loss of $53 per contract, a third of the premium. IV tends to rise when stocks fall, so a short put usually suffers from Delta, Gamma and Vega at the same time.
Vega is larger for longer-dated options and smaller for short-dated ones. That gives the core trade-off in choosing an expiry:
- Short-dated (under 2–3 weeks): high Theta, high Gamma, low Vega. Small moves can wipe out the premium quickly; there is little time to react.
- 30–45 days: moderate Theta, moderate Gamma, moderate Vega. Enough premium to be worth it and enough time to manage.
- 60–90 days: low Gamma, more Vega, slow decay. Calmer day to day, but more exposed to a change in the volatility regime.
Reading the position, not the leg
The Greeks add across legs and contracts. Selling two of the 35-day 95 puts gives a position of about +55 Deltas (like owning 55 shares), Theta of about +$8.80 a day, Gamma of about −7 shares per $1 and Vega of about −$21 per IV point. Thinking in these units answers the questions that matter: how much do I lose if the stock drops $5, and what happens if IV jumps 5 points?
How to apply it
- Entry. Sell 30–45 days to expiry as the default, where premium, Gamma and time to manage are balanced. Choose the short strike by Delta: around 0.30 for covered calls and cash-secured puts, around 0.15–0.20 for each short strike of an iron condor, where two sides must both hold.
- Target. Close at about half of the maximum profit. The remaining half takes longer and comes with more Gamma per dollar earned.
- Stop. Close or roll when the short option's Delta roughly doubles from entry (for example from 0.30 to 0.60), or when the loss reaches about twice the credit.
- Time exit. With about 21 days left, close or roll anything still open, unless you deliberately want assignment, as in the wheel.
- Invalidation. If the position's net Delta has drifted far from what you intended, the trade has become a directional bet you did not plan; reduce it.
In Clear Tape
The strategy builder on the Options page applies these conventions as defaults. Income strategies start from the expiry closest to 35 days within a 20 to 60 day window; short strikes start near 0.30 Delta, or 0.16 for each side of the iron condor, and a Delta control (0.05 to 0.50) moves the strikes to those nearest any target. Each build shows the position's Greeks for one lot in plain words, each leg's Delta, the chance of profit at expiry from a lognormal model at today's IV, and the chance of touching each short strike using the twice-Delta rule. The payoff chart adds Today and In N days lines, drawn assuming IV stays unchanged, so you can see Theta and Gamma at work. The builder is for Pro members and uses the previous session's closing data; it places no orders. See pricing.
Common mistakes
- Selling weekly options for their high Theta without accounting for the Gamma that comes with it.
- Reading Delta as an exact probability, or forgetting that touching a strike is about twice as likely as finishing beyond it.
- Watching only Delta and ignoring Vega, which can produce a loss with the stock unchanged.
- Judging each leg separately instead of adding the Greeks across the whole book.
- Holding to the last day to squeeze out the final cents of premium.
Summary
A short option is paid in Theta and exposed through Gamma and Vega. Theta and Gamma both peak in the final weeks, so the best risk-adjusted part of a short option's life is usually the middle, from about 45 to about 21 days. Delta sets the balance between premium and the chance of being tested, and the position's combined Greeks tell you what a given move or volatility change will cost. The next lesson applies all of this to the two simplest income structures: covered calls and cash-secured puts.
For educational purposes only. Not investment advice.