Map each Greek to a question
| Greek | Question | Typical unit |
|---|---|---|
| Delta | How sensitive to the stock? | Premium dollars/share per $1 stock move |
| Gamma | How quickly does delta change? | Delta change per $1 stock move |
| Theta | What is one day’s estimated time effect? | Premium dollars/share per day |
| Vega | How sensitive to implied volatility? | Premium dollars/share per 1 IV percentage point |
| Rho | How sensitive to rates? | Premium dollars/share per 1 rate percentage point |
Model inputs and quoting conventions vary. A displayed theta can be annualized or daily; rates and volatility can be expressed in decimals or percentage points. Multiplying an already scaled position Greek by 100 again produces an error.
Combine a local scenario
One local estimate, several moving parts
Read the chart data
| Measure | USD per share |
|---|---|
| Delta effect | 1.1 |
| Gamma effect | 0.08 |
| Theta effect | -0.08 |
| Vega effect | -1.2 |
| Total estimate | -0.1 |
For the fictional call, stock rising $2 helps through delta and gamma, but a 10-point drop in IV more than offsets that price benefit after a day of decay. The net estimate is −$0.10 per share, or −$10 for one standard long contract. This demonstrates competing effects; it is not a reliable repricing over such a large IV move.
Scale and sign the position
Two long standard contracts multiply per-share sensitivities by 200. A short position reverses signs. A portfolio adds the signed exposures of its legs, but small net delta can coexist with substantial gamma, vega or assignment exposure.
A local approximation is ΔV ≈ delta×ΔS + ½×gamma×ΔS² + theta×days + vega×IV-point change + rho×rate-point change. It omits higher-order and cross effects and assumes the quoted units. A real model recalculates as the inputs move.
Use Greeks as a map of sensitivity
A Greek is neither a promised return nor a complete risk measure. Gaps, liquidity, bid–ask spreads, exercise and changes in volatility shape results. Near expiration, sensitivities can change rapidly, making stale values particularly unhelpful.
Read each individual Greek lesson, then return to the combined example. Write down which inputs changed and which were assumed constant before attributing a loss entirely to “time decay” or a gain entirely to getting direction right.
A per-share vega is 0.12 and you own two standard contracts. What is a +1 IV-point local effect?
Show the explanation
About 0.12 × 100 × 2 = $24, other inputs fixed. This assumes the display is per share and per one percentage point, rather than an already scaled position value.
Sources and editorial notes
Original explanations and hypothetical examples prepared with AI assistance. Primary reference check dates are listed below. Numerical examples are hypothetical unless explicitly identified otherwise.
- OCC / OIC: Understanding Options Greeks
Greeks are theoretical local sensitivity estimates, not guaranteed price changes. Checked October 17, 2026.
- OCC / OIC: Delta
Definition, sign and conventional units for this sensitivity. Fixed-input arithmetic, scenarios and visuals are original and explicitly local. Checked October 17, 2026.
- OCC / OIC: Gamma
Definition, sign and conventional units for this sensitivity. Fixed-input arithmetic, scenarios and visuals are original and explicitly local. Checked October 17, 2026.
- OCC / OIC: Theta
Definition, sign and conventional units for this sensitivity. Fixed-input arithmetic, scenarios and visuals are original and explicitly local. Checked October 17, 2026.
- OCC / OIC: Vega
Definition, sign and conventional units for this sensitivity. Fixed-input arithmetic, scenarios and visuals are original and explicitly local. Checked October 17, 2026.
- OCC / OIC: Rho
Definition, sign and conventional units for this sensitivity. Fixed-input arithmetic, scenarios and visuals are original and explicitly local. Checked October 17, 2026.