⚡ Black-Scholes Options Pricer

Professional options pricing calculator with advanced grid visualization

Call Option Price
$0.00

Option Parameters

%
%
%

The Greeks

Delta (Δ)
0.0000
Gamma (Γ)
0.0000
Theta (Θ)
0.0000
Vega (ν)
0.0000
Rho (ρ)
0.0000

Price Grid Heatmap

Visualize option prices across different stock prices (horizontal) and volatilities (vertical)

±10%
±5%

Click "Simulate Grid" to generate heatmap

The History of the Black-Scholes Formula

The Black-Scholes model is one of the most important contributions to modern financial theory, revolutionizing the derivatives market since its publication in 1973. This groundbreaking formula was developed by Fischer Black and Myron Scholes, with significant contributions from Robert Merton.

🏆 Nobel Prize Recognition

In 1997, Myron Scholes and Robert Merton were awarded the Nobel Prize in Economic Sciences for their method to determine the value of derivatives. Fischer Black had passed away in 1995, but his contributions were acknowledged in the prize citation.

📈 Market Impact

The formula enabled the explosive growth of the derivatives market, which today represents trillions of dollars in notional value. It provided the first complete mathematical framework for pricing European options.

The model makes several key assumptions: constant volatility, constant risk-free rate, log-normal distribution of stock prices, no dividends during the option's life (later extended), and the ability to trade continuously without transaction costs.

The Famous Formula

Call Option: C = S₀ × N(d₁) - K × e^(-rT) × N(d₂)
Put Option: P = K × e^(-rT) × N(-d₂) - S₀ × N(-d₁)

Where: d₁ = [ln(S₀/K) + (r + σ²/2)T] / (σ√T)
And: d₂ = d₁ - σ√T

This elegant mathematical relationship connects an option's price to five key variables: current stock price (S₀), strike price (K), time to expiration (T), risk-free rate (r), and volatility (σ).

Today, the Black-Scholes model remains the foundation for options pricing, though practitioners have developed numerous extensions and improvements to address its limitations, including stochastic volatility models and jump-diffusion processes.

Use our calculator above to explore this Nobel Prize-winning formula and see how changes in market parameters affect option prices and the Greeks in real-time.