Tier 2 · Essentials · Options · Module OP.1
The Greeks
Delta, gamma, theta, vega, and rho explained in plain language — how each changes an option's price, how time decay accelerates, and why implied volatility can make you lose money even when you're right.
Lesson 2 of 2 · 6 min read
An option's price changes for more reasons than the underlying moving up or down. Time passing, volatility rising or falling, and even interest rates all affect it. The Greeks measure each of these sensitivities. You don't need to calculate them — every options platform shows them — but you do need to understand them, because they explain the most common and frustrating options experience: being right about direction and still losing money.
What you'll learn
- Delta — sensitivity to the underlying price
- Gamma — how delta itself changes
- Theta — time decay, and why it speeds up near expiry
- Vega — sensitivity to implied volatility, and "IV crush"
- Rho — sensitivity to interest rates
- How to read the Greeks together before a trade
1. Delta: price sensitivity
Delta estimates how much the option price changes for a $1 move in the underlying.
| Option | Typical delta range |
|---|---|
| Call | 0 to +1 |
| Put | 0 to −1 |
| At the money | Around ±0.50 |
| Deep in the money | Close to ±1 (moves almost like the shares) |
| Far out of the money | Close to 0 (barely moves) |
(Illustrative.) A call with delta 0.40. The stock rises $2 → the option gains about $0.80 per share, or $80 per contract (× 100).
Delta is also a rough, informal guide to the probability that an option expires in the money — a 0.20-delta option is, loosely, around a 20% chance.
2. Gamma: how delta changes
Gamma measures how much delta changes for a $1 move in the underlying.
- Gamma is highest for at-the-money options near expiry.
- High gamma means delta — and therefore the option's behaviour — can change very quickly.
That's why short-dated at-the-money options can swing from almost worthless to very valuable (or the reverse) within hours.
3. Theta: time decay
Theta estimates how much value an option loses per day as time passes, all else equal.
(Illustrative.) Theta of −0.05 → the option loses about $0.05 per share per day, or $5 per contract per day.
Time decay accelerates as expiry approaches, especially for at-the-money options. An option with 60 days left loses time value slowly; with 5 days left, it can lose it rapidly.
| Effect of theta | |
|---|---|
| Option buyers | Pay theta every day — time works against you |
| Option sellers | Collect theta every day — time works for you |
4. Vega: volatility sensitivity
Implied volatility (IV) is the market's expectation of future volatility, backed out from option prices. Higher IV → more expensive options.
Vega estimates how much the option price changes for a 1 percentage-point change in IV.
IV crush
Before scheduled events — especially earnings (see Earnings season and how stocks react) — IV rises as the market prices in a big move. Right after the event, uncertainty disappears and IV collapses. This is IV crush.
Worked example
(Illustrative.) Before earnings, a stock trades at $100. You buy a $100 call for $6.00 (IV 60%). Earnings are good: the stock opens at $104.
- Intrinsic value is now $4.
- IV falls from 60% to 30% — much of the remaining time value evaporates.
- The option is now worth about $5.00.
Result: the stock rose 4% in your direction, and you lost $100 per contract. The move was smaller than the implied move the market had priced in.
5. Rho: interest-rate sensitivity
Rho measures sensitivity to interest rates. For short-dated options it's usually small; it matters more for long-dated options. Higher rates tend to raise call prices slightly and lower put prices slightly.
6. Reading the Greeks together
| Greek | Question it answers | Long option | Short option |
|---|---|---|---|
| Delta | How much do I gain or lose if the price moves? | Directional exposure | Opposite exposure |
| Gamma | How fast will that exposure change? | Helps (moves accelerate gains) | Hurts (moves accelerate losses) |
| Theta | What does a day cost me? | Costs you | Pays you |
| Vega | What if volatility changes? | Gains if IV rises | Gains if IV falls |
Common beginner mistakes
- Ignoring theta on short-dated options.
- Buying options into earnings without accounting for IV crush.
- Assuming a 0.50-delta option moves $1 for every $1 in the stock — it moves about half that.
- Forgetting that Greeks change as price, time, and volatility change.
- Selling options for theta without respecting gamma risk near expiry.
Key terms
| Term | Meaning |
|---|---|
| Delta | Option price change per $1 move in the underlying |
| Gamma | Change in delta per $1 move in the underlying |
| Theta | Option value lost per day from time decay |
| Vega | Option price change per 1-point change in implied volatility |
| Rho | Option price change per 1-point change in interest rates |
| Implied volatility | The volatility the market is pricing into options |
| IV crush | A sharp fall in implied volatility after an event |
Practice
- On an option chain, compare the delta, theta, and vega of an ATM option with 7 days and 60 days to expiry.
- Calculate how much each would lose per contract over 5 days from theta alone.
- Before the next earnings report on a stock you follow, record the IV of an ATM option. Record it again the day after. How much did it fall?
- Write your "one sentence per Greek" risk summary for a hypothetical trade.
Quick recap
- Delta = sensitivity to price; ATM options are around ±0.50.
- Gamma = how fast delta changes; highest near expiry for ATM options.
- Theta = daily time decay, accelerating near expiry — a cost for buyers.
- Vega = sensitivity to implied volatility; beware IV crush after events.
- Being right on direction isn't enough — time and volatility matter too.
Educational content only — not financial advice. Trading involves substantial risk of loss. Practise on a demo account before risking real money.
