Live price for a reference stock
What each Greek tracks
| Greek | Tracks | Direction for long buyer | Plain-English one-liner |
|---|---|---|---|
| Delta | Stock price move | Helps when stock moves your way | How much the option moves per $1 in the stock |
| Theta | Time passing | Hurts every day | The daily rent you pay for holding optionality |
| Vega | Implied volatility change | Helps when IV rises, hurts when IV falls | How much the option moves per 1 percentage-point change in implied vol |
| Gamma | How fast delta changes | Helps long buyers, hurts short sellers | The curvature — the option's directional bet gets stronger as the stock moves toward strike |
Estimating an option's move from delta
Expected Option Move = Delta × Stock Move
How delta varies across moneyness
A delta of 0.50 means the option moves ~$0.50 per $1 stock move. Deep ITM options have delta near 1.0; far OTM options have delta near 0. (Delta also doubles as the rough probability of finishing in-the-money — that's the moneyness lens from the previous module.)
Time decay, step by step
Theta (time decay) is the silent tax on option buyers. An ATM option with 30 days to expiration might lose $0.05–$0.15 per day. With 5 days left, that accelerates dramatically. This is why holding short-dated OTM options to expiry is usually a losing proposition.
| Days to Expiration | Theta (daily loss) | Cumulative Decay |
|---|---|---|
| 60 days | ~$0.03/day | Slow bleed |
| 30 days | ~$0.06/day | Noticeable |
| 7 days | ~$0.15/day | Accelerating rapidly |
| 1 day | All remaining time value | Gone by close |
Compare delta across the options chain
What theta does while the stock is flat
Theta as the seller's structural edge
When theta overwhelms a low-delta call
Vega: sensitivity to implied volatility
Vega measures how much an option's price moves per 1-percentage-point change in implied volatility (the market's expectation of future movement). Long options are long vega: rising IV helps you, falling IV hurts. This is why a stock can move your way after earnings and the option still loses value — the post-event collapse in IV (the 'IV crush') overwhelms the directional gain. Buying an option is a bet on movement AND on volatility staying elevated.
Gamma is the trap
Gamma is the trap. Gamma measures how fast Delta itself changes as the stock moves. Option buyers are long gamma — their directional bet strengthens in their favor. Option sellers are short gamma — their exposure gets worse exactly when the stock moves against them. A short call that started roughly delta-neutral can become deeply short the stock if it rallies through the strike. Gamma risk is why writing naked options is dangerous in a way that buying them is not. (The full position-Greeks math lives in the advanced Options 301 path; here, just know the sign: long options = long gamma, short options = short gamma.)
How gamma shifts delta-equivalent exposure
Where to go next for per-Greek depth
This module is the map; four companion lessons in this path are the territory, and each one assumes only what you have read here. Delta in Depth separates the three readings that live inside one number: rate of change, rough odds of finishing in the money, and share-equivalent exposure. Theta in Depth replaces the phrase 'decay accelerates' with a decay table and a square-root rule you can apply to any quote, then shows how a correct directional call can still finish under water. Gamma in Depth explains why a buyer's gain beats the straight-line delta estimate and why a writer's exposure grows exactly when it hurts. Vega in Depth closes the set with the volatility half of the premium and the earnings-week collapse that punishes buyers who were right about direction. Take them in that order. If only one is going to fit into your week, make it Theta — it is the Greek that bills every position, every day, whether or not anything happens.
Sit with the ideas.
You own a call option with delta 0.40 and theta -$0.05. The stock rises $2 and one day passes. Approximately what happens to your option's value?