The Greeks estimate how an option's price changes when one thing changes and everything else stays the same. They come from a pricing model (usually Black–Scholes or a variant). They're estimates, but they're the language every options desk uses.
Delta: direction
- How much the option's price changes for a $1 move in the stock. Calls run from 0 to +1.00; puts from 0 to −1.00.
- A +0.50 delta call gains about $0.50 per share ($50 per contract) when the stock rises $1.
- ATM options sit near ±0.50; deep ITM near ±1.00; far OTM near 0.
- Delta is also a rough, market-implied estimate of the chance the option finishes ITM. A 0.20 delta call is roughly a 1-in-5 shot.
- Share-equivalent: 1 contract × delta × 100. Ten 0.30-delta calls act like about 300 shares for small moves.
Gamma: how fast delta changes
- How much delta changes for a $1 move in the stock.
- Highest for ATM options close to expiration. That's why weekly options can go from worthless to doubling in an hour.
- Long options are long gamma (moves help you more the bigger they get). Short options are short gamma (big moves hurt more and more).
Theta: time decay
- How much value the option loses per day, all else equal. Theta of −0.05 means about −$5 per contract per day.
- Grows as expiration nears, especially for ATM options.
- Buyers pay theta; sellers collect it.
Vega: volatility
- How much the option's price changes for a 1 percentage point change in implied volatility.
- Vega of 0.12 means the option gains about $12 per contract if IV rises from 30% to 31%.
- Longer-dated options have more vega. This is why LEAPS react strongly to IV changes and weeklies barely do.
Rho: interest rates
- Change for a 1 point move in rates. Small for short-dated options; it matters for LEAPS.
Reading a whole position. Add up the Greeks of each leg, times contracts:
- Long call: +delta, +gamma, −theta, +vega. You want a big move, soon, ideally with IV rising.
- Long put: −delta, +gamma, −theta, +vega.
- Covered call: shares (+100 delta) plus a short call (−delta, −gamma, +theta, −vega). Less upside exposure, collecting time decay.
- Short put: +delta, −gamma, +theta, −vega. You want calm, sideways-to-up markets and falling IV.
Worked example. A 45-day $100 call costs $4.20 with delta 0.52, gamma 0.03, theta −0.06 and vega 0.15. Tomorrow the stock rises $2 and IV is unchanged. Estimate: +$2 × 0.52 ≈ +$1.04, plus a small gamma boost (about +$0.06), minus one day of theta (−$0.06). New price is about $5.24.
Key takeaways
- Delta = direction, gamma = acceleration, theta = rent, vega = sensitivity to fear.
- Buyers are long gamma and vega and pay theta. Sellers are the opposite.
- Add up the Greeks across legs to see what a position really wants.