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| 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 |
Formula
Expected Option Move = Delta × Stock Move
Key point
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.)
Step through
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 |
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Key insight
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Key point
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.
Key point
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.)
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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?