Greeks Visualizer
Chart a European option's value and Greeks against the spot price, the time to expiry or volatility, and compare the same option closer to expiry.
Learning focus: each Greek is a slope of the value surface, so it has a shape: gamma, vega and theta are largest near the money, and gamma and theta concentrate there as expiry approaches.
Value curves upward (convexity), and the gap above intrinsic value is widest near the strike.
Delta is the slope of the value curve; it turns fastest near the strike.
Gamma is a hump near the strike (usually a little below it), and it grows taller and narrower as expiry nears.
Vega is largest near the money, where volatility most changes the chance of finishing in the money.
Theta is most negative near the money, where there is the most time value to lose.
A call's rho grows as it moves into the money; a put's rho grows more negative.
The dot marks your inputs. Vega and rho are per percentage point, theta per calendar day, all for the whole position.
- Gamma peaks at a spot price of 89.58, a little below the strike of 100.00: delta changes fastest for an option near the money.
- At the money (S = K = 100.00), delta is 0.6368 per option, not exactly 0.5: the drift (r − q + σ²/2)T pushes d₁ above zero.
- Theta is most negative near a spot price of 107.25: time decay costs most when the outcome is most uncertain.
- Delta runs from 0.0009 at a spot of 50.00 to 0.9913 at 150.00.
- With 0.10 years left instead of 1.00, gamma at the strike (100.00) is 0.0627 against 0.0188 (3.34 times as large), and theta per day is −0.0414 against −0.0176.