CFA derivatives tool

Black-Scholes + Greeks Visualizer

Price European calls and puts, then inspect how delta, gamma, vega, theta, and rho move as market inputs change.

Examples

Load an option scenario

Inputs

Option price
$10.45

call value

Delta
0.6368

Spot sensitivity

Gamma
0.01876

Delta curvature

Vega
0.3752

Per 1 vol point

Theta annual
-$6.4140
Theta daily
-$0.0176
Rho
0.5323

Per 1 rate point

d1 / d2
0.35 / 0.15
Live interpretation
  • The call is priced at $10.45 with moneyness S/K of 1.00.
  • Delta is 0.6368, so a $1 spot move changes the option by roughly $0.6368 before gamma effects.
  • Gamma is 0.01876 and is usually most important near the strike and near expiration.
  • Vega is 0.3752 per volatility point; theta is -$0.0176 per day.

Option price vs spot

Option price versus stock price$50$75$100$125$150-$5$11$27$44$60SpotOption value
Current option value
Hover or focus a point to inspect the curve.

Payoff at expiration

Option payoff at expiration$50$75$100$125$150-$5$10$25$40$55Spot at expirationIntrinsic value
Expiration payoff
Hover or focus a point to inspect the curve.

Greeks mini curves

Each curve changes one input at a time while holding the others fixed.

Delta vs spot$50$75$100$125$150-0.09910.19830.49560.7931.0904SpotDelta
Delta vs spot
Hover or focus a point to inspect the curve.
Gamma vs spot$50$75$100$125$150-0.00220.00430.01080.01730.0238SpotGamma
Gamma vs spot
Hover or focus a point to inspect the curve.
Vega vs volatility7.0%13.5%20.0%26.5%33.0%-0.03790.07590.18970.30360.4174VolatilityVega
Vega vs volatility
Hover or focus a point to inspect the curve.
Theta vs time0.10 yrs0.45 yrs0.80 yrs1.15 yrs1.50 yrs-16.6323-12.0962-7.5601-3.02411.512TimeTheta
Theta vs time
Hover or focus a point to inspect the curve.
Rho vs rate2.0%3.5%5.0%6.5%8.0%-0.0570.11410.28520.45630.6274RateRho
Rho vs rate
Hover or focus a point to inspect the curve.

Spot-volatility sensitivity heatmap

Cells show price change versus the current option value.

Hover or focus a cell to inspect the diagnostic value.

Current formula outputs

MeasureValue
d10.35
d20.15
Price$10.45
Delta0.63683
Gamma0.018762
Vega0.37524
Theta annual-$6.41403
Theta daily-$0.01757
Rho0.53232

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FAQ

Does this calculator support dividends?

Yes. The Black-Scholes inputs include a continuous dividend yield q, so the price and Greeks use dividend-discounted spot value.

Are Greeks shown per one percent change?

Vega and rho are shown per one percentage point change in volatility or rates. Theta is shown both annualized and per day.

Can this price American options?

No. Black-Scholes in this page is for European calls and puts. Use the binomial option pricing visualizer for American exercise logic.