You own a call with theta of −0.03 on the options screen. You are thinking of holding it for one more day. Does waiting cost three cents or about $3?
Beside it sit delta 0.55, vega 0.10 and gamma 0.04. The four numbers separate the effects of a stock move, another day and changing volatility. Gamma adds a twist: it measures how delta itself changes.
A decimal without its unit tells you very little about the money in your account.
Four numbers with different jobs
Option Greeks are estimates from a pricing model of how an option responds to small changes. They are local sensitivities, describing what happens near the current stock price, time remaining and volatility.
Use the original snapshot: Harbor Coffee, our fictional coffee business, at $66 and the 60-day $65 call at $4. Add an implied volatility of 30%. The option quote and rounded Greeks are invented for teaching, not calculated from a pricing model.
The pricing lesson let several inputs change together. Here, each Greek estimate changes one input from this snapshot and holds the others fixed. IV is short for implied volatility. The table is a unit key:
| Greek | Input change | Quote | Estimated effect |
|---|---|---|---|
| Delta | Stock +$1 | 0.55 | +$0.55/share |
| Theta | 1 calendar day | −0.03 | −$0.03/share |
| Vega | IV 30% → 31% | 0.10 | +$0.10/share |
| Gamma | Stock +$1 | 0.04 | Delta +0.04 |
The standard 100-share multiplier turns the theta row into −$0.03 × 100 = −$3 for one calendar day.
Three cents per share becomes about $3 for the contract. Small quoted numbers do not mean small dollar exposure.
Delta and gamma follow the stock
Delta estimates the change in premium per share for a $1 move in the stock.
A rise from $66 to $67 gives 0.55 × $1 ≈ $0.55 more premium per share, or $55 for one contract. The ≈ sign means "about": delta itself can change during the move. A $1 fall gives a starting estimate of −$0.55 per share, or −$55.
Plain calls you own have deltas between 0 and 1; puts between −1 and 0. The minus sign on a put means a stock rise pushes its value down. A delta closer to either 1 or −1 means a larger dollar response than one near zero. Bigger sensitivity means more exposure, not a better grade.
Gamma estimates how much delta changes per $1 stock move.
Here, 0.55 + 0.04 × 1 = 0.59. Delta moves toward 0.59 as the stock rises that dollar. The markers show the small shift along the call's full 0–1 range. The +0.04 is a change in delta, not another $0.04 to add to the premium.
Gamma can be especially large when the stock is near the strike close to expiration. A small stock move can then change delta quickly. Two options with the same delta can stop behaving alike if their gammas differ. Owning one share, by comparison, gives a constant delta of 1.
Theta and vega follow time and volatility
Theta measures how the premium responds to time passing. Our −0.03 means a day's passage reduces the $4 premium to about $3.97 per share. That $3 contract loss is a change in value, not a fee taken from your cash balance.
Calls and puts you buy usually have negative theta. Time decay can become faster near expiration when the stock is near the strike. Multiplying −$3 by all 60 remaining days gives −$180, but that is not a valid forecast: theta changes along the way.
Vega measures the premium's sensitivity to a one-percentage-point change in IV. A move from 30% to 31% gives 0.10 × 1 ≈ $0.10 more premium per share, or $10 for the contract. The $4 premium becomes about $4.10.
That is one percentage point. A 1% relative increase from 30% would reach only 30.3%. Vega uses the first kind of change.
A flat stock does not mean a flat option price. The calendar keeps moving, and volatility can change without a stock rally or fall.
More time often means more dollar vega. Compare calls on the same stock at the same strike, quoted in the same units: the later expiration tends to be more sensitive to an IV change. Two identical contracts also carry twice the exposure of one, even though the screen quotes the same Greeks.
Writing the call, meaning opening a short position, reverses the signs of its Greeks. Time decay then favors the seller, while a stock rise or an IV increase works against them. The covered-call lesson explains the obligation behind that premium income.
Where the estimates stop helping
Real inputs move together, and the Greeks change with them. After a large earnings jump, the old sensitivities describe a place the option has already left. A $1 estimate cannot safely be stretched across a $10 move.
The bid-ask spread can matter more than a small theoretical change. Say the call has a $3.90 bid and a $4.10 ask. That $0.20 gap is $20 per contract, far larger than the $3 time effect. A model's price is not a promise of an execution price.
Delta 0.55 does not give you a 55% chance of profit. What you paid, when you exit and what you receive all affect the result.
At the same $4 quote, someone who paid $3 has a $1 per-share gain; someone who paid $5 has a $1 loss, before costs. Same option, same delta, opposite profit records.
For your one-day wait, theta isolates about $3 of lost value on the contract. A stock or volatility move can outweigh it. You have priced the effect of time passing, not predicted tomorrow's total gain or loss.
In short
- Delta estimates a small stock move's effect on the option premium.
- Gamma tells you how delta changes as the stock moves.
- Daily theta is not a decay schedule; vega uses IV percentage points.
- Multiply per-share price effects by 100 for a standard US stock-option contract.
- Greeks describe changing sensitivities, not your odds of profit or tomorrow's price.