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Theta
Theta estimates the option-price change associated with one day passing while other inputs are unchanged.
Lesson · Options Trading
Theta and Vega
Combine time decay and implied-volatility sensitivity, compare linear Greek estimates with full theoretical repricing, and identify interaction effects.
Synthetic educational examples
Core concepts
Theta prices a day; vega prices an IV point; both are local to the current state.
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Vega
Vega estimates the option-price change for a one-percentage-point change in implied volatility.
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Local estimates
Greeks describe sensitivity at the current state and must be recalculated after meaningful changes.
Worked example
The 100 call, 45 DTE, IV 35%, stock held at $100; five days pass and IV falls 10 points — the lab’s default state, attributed line by line.
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Theta −0.060 per share per day: −0.060 × 5 days × 100 = −$30.Theta is per share; the contract figure is × 100. Five days of it is the time contribution.
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Vega 0.139 per IV point: 0.139 × (−10) × 100 = −$139.Ten points, not 0.10. Vega is quoted per one percentage point of IV.
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Linear estimate: −$30 − $139 = −$169. Full repricing: $5.17 → $3.54, −$162.The +$7 residual is the Greeks changing as the state changed: theta and vega at 40 DTE and 25% IV are not what they were at 45 and 35.
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Both signs are against the holder here; the writer’s attribution is the mirror image.Time passing and IV falling both transfer value from the long side to the short side.
Interactive lesson
Apply days passed and an IV-point change, and compare the linear attribution with the repriced change.
IV −10 pointsCurrent IVIV +10 points
Evaluate theta and vega together
A long option can be directionally correct yet lose value when time and IV move against it.
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Read current theta
Estimate the cost of waiting under unchanged model inputs.
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Read current vega
Estimate the sensitivity to an IV-point change.
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Stress time and IV
Test several combinations rather than a single expected case.
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Reprice the full position
Use linear estimates for intuition and a full model for a better approximation.
Theta and vega
Score 0 / 0Choose the best answer.
Lesson rule
Change the inputs, calculate the result, and explain the risk before selecting a contract.
Common mistakes
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Multiplying theta indefinitelyTheta is not constant and changes as expiration approaches.
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Using IV change as a decimal with quoted vegaVega is usually stated per one IV percentage point, so units must match.
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Adding Greek estimates as exact P/LCross-effects and changing sensitivities create differences from linear estimates.
Completion standard
✓
Finish when you can attribute a premium change to theta × days and vega × IV points in the right units, and say why the sum is an estimate rather than the P/L.
The drill asks for the attribution with the lesson’s own defaults; the unit trap — points, not decimals — is in it.
Model scope: Theoretical values use a simplified European Black–Scholes model with a fixed 4.5% annual rate and no dividend input, so a number here can be reproduced in any calculator that takes those inputs. Listed products, early exercise, dividends, spreads, fees, and market conditions can produce different prices and outcomes.