# Black-Scholes + Greeks Visualizer Free Black-Scholes option calculator with delta, gamma, vega, theta, rho, payoff diagram, sensitivity curves, and spot-volatility heatmap. Canonical URL: https://exclam.ai/cfa/black-scholes-greeks-calculator/ CFA derivatives tool Price European calls and puts, then inspect how delta, gamma, vega, theta, and rho move as market inputs change. Examples ## Load an option scenario Baseline At-the-money European call Load Clean setup for connecting d1, d2, price, delta, gamma, vega, theta, and rho. Start here to see balanced moneyness and high gamma. Downside Out-of-the-money put Load A put with negative delta and lower intrinsic probability, useful for seeing put Greeks signs. Delta should be negative and rho should usually be negative. Volatility High-volatility growth call Load Higher volatility expands the option value and vega effect across the spot curve. Compare vega and the price curve against the baseline. Theta Short-expiry at-the-money option Load Near-expiration option where gamma and daily theta become more pronounced. Useful for seeing time decay and curvature pressure. Dividend Dividend-sensitive put Load Continuous dividend yield changes spot discounting and option sensitivity. Use this to see how q changes price and delta. ## Inputs Option typeStock priceStrike priceTime to expiration years Risk-free rate % Dividend yield % Volatility % 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 Figure: Option price versus stock price Current option value Hover or focus a point to inspect the curve. ## Payoff at expiration Figure: Option payoff at expiration 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. Figure: Delta vs spot Delta vs spot Hover or focus a point to inspect the curve. Figure: Gamma vs spot Gamma vs spot Hover or focus a point to inspect the curve. Figure: Vega vs volatility Vega vs volatility Hover or focus a point to inspect the curve. Figure: Theta vs time Theta vs time Hover or focus a point to inspect the curve. Figure: Rho vs rate 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. Price change 75% vol 100% vol 125% vol 150% vol 80% spot -$9.65-$8.59-$7.31-$5.90 90% spot -$7.11-$5.36-$3.58-$1.79 100% spot -$1.86$0.00$1.89$3.78 110% spot $5.78$7.21$8.85$10.61 120% spot $14.85$15.72$16.96$18.43 Hover or focus a cell to inspect the diagnostic value. ## Current formula outputs | Measure | Value | | --- | --- | | d1 | 0.35 | | d2 | 0.15 | | Price | $10.45 | | Delta | 0.63683 | | Gamma | 0.018762 | | Vega | 0.37524 | | Theta annual | -$6.41403 | | Theta daily | -$0.01757 | | Rho | 0.53232 | Related calculators ## CFA finance tools [CFA hub](https://exclam.ai/cfa/index.md) [BA II Plus-style calculator TVM, cash-flow, amortization, NPV, and IRR practice with algebraic entry. All levels Calculator keystrokes](https://exclam.ai/cfa/ba-ii-plus-calculator/index.md) [HP 12C-style calculator RPN arithmetic and core financial calculator workflows in the browser. All levels RPN practice](https://exclam.ai/cfa/hp12c-calculator/index.md) [Binomial option pricing visualizer Stock tree, option tree, risk-neutral probability, delta, and American exercise nodes. Level II Option trees](https://exclam.ai/cfa/binomial-option-pricing-calculator/index.md) [Bond price, yield, and duration calculator Bond pricing, YTM, Macaulay duration, modified duration, convexity, and DV01. Levels I-II Bond math](https://exclam.ai/cfa/bond-price-yield-duration-calculator/index.md) [Fixed income immunization tool Match asset and liability duration, then stress price risk and convexity cushion. Levels II-III Duration matching](https://exclam.ai/cfa/fixed-income-immunization-calculator/index.md) [Brinson attribution calculator Allocation, selection, interaction, waterfall, and active return reconciliation. Level III Performance attribution](https://exclam.ai/cfa/brinson-attribution-calculator/index.md) ## 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.