The option Greeks
Use the Greeks to explain how stock moves, time, volatility, and rates affect an option position. Learn the units, signs, and limits of these local estimates, then combine the option with shares and other positions.
By OptionsKing. Publisher and editorial methods.
Learning path
Begin with delta, gamma, theta, and vega. Then study short-position signs and the distinction between an option leg and the whole strategy.
Apply those ideas to probability approximations, changing decay curves, and portfolio exposure. You should be able to state both what a Greek estimates and which assumptions make that estimate unreliable.
Compare time-decay curves for two strikes (6:38 on YouTube).
Lessons
- Black-Scholes explained: inputs, IV and model limitationsUse Black-Scholes as a translator between price, volatility and sensitivity. Its assumptions define what the output can explain.
- Delta explained: sensitivity, share equivalents and probabilityDelta is a local price sensitivity. Convert it into position exposure while keeping its probability interpretation separate.
- Delta vs probability: finish, touch and model assumptionsDelta and finish probability are different model quantities. Distinguish them from touch probability and real-world outcomes.
- Gamma explained: changing delta and near-expiration riskGamma describes how delta changes. It helps explain why near-strike positions can become much more sensitive close to expiration.
- Theta explained: time sensitivity is not daily incomeTheta estimates the effect of passing time with other inputs unchanged. It is a sensitivity, not a daily cash payment.
- Nonlinear theta decay: at-the-money vs out-of-the-money optionsDecay changes with moneyness and time. Compare two fixed-input curves to understand why a distant option can run out of value early.
- Vega explained: sensitivity to implied volatilityVega measures local sensitivity to implied volatility. Combine it with stock and time effects before interpreting a marked option loss.
- Rho explained: interest-rate sensitivity and maturityRho measures sensitivity to interest rates. Put it in context with maturity, stock exposure and the return on reserved cash.
- Vanna, charm and vomma: how sensitivities changeSecond-order Greeks describe changing sensitivities. Use them to understand why today's hedge may not remain the same tomorrow.
- Short-option Greeks: signs and combined positionsReverse the Greek signs when reversing an option position, then add the stock and other legs to measure the exposure actually held.
- Portfolio delta: share equivalents, dollar exposure and scenariosPortfolio exposure needs both signed deltas and comparable units. Use dollar delta for a stated common percentage-move scenario.
- Put-call parity: equivalent payoffs and financingPut-call parity links matching European call and put prices with stock and financing. Understand the payoff identity before applying it to quotes.
From one contract to a position
The running example sells one $72.50 call against 100 shares of UBER at $68.40. An illustrative call delta of 0.331 means a short-call delta of -33.1 share-equivalents; combined with the shares, the covered call starts near +66.9.
These are local sensitivities, not fixed exposure throughout the trade. Large moves, changing IV, and approaching expiration alter the Greeks. Theta is not guaranteed daily income, and delta is neither an observed win rate nor an assignment forecast.
Common questions
Which Greeks should I start with?
Delta estimates price sensitivity, gamma its rate of change, theta the effect of time with other inputs fixed, and vega sensitivity to IV. Learn their units before comparing numbers.
What changes when I sell an option?
The option leg's Greeks reverse sign. The Greeks of a covered call also include the shares, so its net delta differs from that of a naked short call.
Does decay always accelerate near expiration?
No. The shape depends on moneyness and other inputs. An at-the-money option and a far-out-of-the-money option can have very different decay curves.
Is delta the probability of finishing in the money?
Not exactly. In a basic European model, delta and the risk-neutral in-the-money probability use different expressions. Neither is automatically a real-world probability.
Run your own numbers
Sources
Rules and thresholds above were checked against these documents on October 17, 2026. Exchange and broker rules change. Confirm anything you are about to act on with your own broker.