Options Greeks
Definition
The “Greeks” are risk measures describing how an option’s price responds to changes in its pricing-model inputs (underlying price, volatility, time, interest rate). They let traders monitor and hedge a portfolio’s risk profile. All but Vega are named for Greek letters.
Core Ideas
| Greek | Measures sensitivity to | Notes |
|---|---|---|
| Delta | $1 move in the underlying | Call 0→1, put −1→0; ATM ≈ ±0.5; also ≈ probability of finishing in-the-money |
| Gamma | rate of change of Delta | Largest at-the-money; the “second derivative”; key for continuous hedging |
| Theta | passage of time | Erodes only extrinsic value; increasingly negative near expiration |
| Vega | 1% change in implied volatility | Greatest at-the-money; long options are long Vega |
| Rho | 1% change in interest rates | Grows with underlying price and time to expiration |
Worked intuition
For a $35.90 stock, $40 strike, 4% rate, 38.8% IV, 38 days: call ≈ $0.54, Delta 0.22 (≈22% chance of expiring ITM), Gamma 0.066 (Delta rises ~6.6¢ per $1 move), Theta −0.018 (loses ~1.8¢/day), Vega 0.034 (+3.4¢ per +1% IV), Rho 0.008. Inputs rarely move in isolation, so real risk is the combined effect.
Relationships
- Options Strategies — the Greeks drive strategy selection and adjustment (e.g. short strangles are short Vega, long Theta)
- Gamma Exposure and Dealer Positioning — Delta and Gamma scaled by Open Interest across the whole chain, used to infer dealer hedging and forecast whether volatility gets suppressed or amplified
- Open Interest and Volume — the position count each Greek is multiplied by to get a market-wide exposure
- Portfolio Risk Management — Greeks are the risk primitives for an options book
- Trading & Finance
References
- The Greeks (Coursera / OIC)